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<title>LaTeX syntax for mathematics</title>
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<main id="latex-syntax-for-mathematics">
<h1 class="title">LaTeX syntax for mathematics</h1>

<div class="topic abstract" role="doc-abstract">
<p class="topic-title">Abstract</p>
<p>Docutils supports mathematical content with a <a class="reference external" href="https://docutils.sourceforge.io/docs/ref/rst/directives.html#math">&quot;math&quot;
directive</a> and <a class="reference external" href="https://docutils.sourceforge.io/docs/ref/rst/roles.html#math">role</a>. The input format is <em>LaTeX math
syntax</em><a class="brackets" href="#math-syntax" id="footnote-reference-1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> with support for literal Unicode symbols.</p>
</div>
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in ``docutils/docs/*/`` sub-sub-diretories.

Attention: this is not a standalone document. -->
<nav class="contents" id="contents" role="doc-toc">
<p class="topic-title">Contents</p>
<ul class="auto-toc simple">
<li><p><a class="reference internal" href="#inline-formulas-and-displayed-equations" id="toc-entry-1"><span class="sectnum">1 </span>Inline formulas and displayed equations</a></p></li>
<li><p><a class="reference internal" href="#mathematical-symbols" id="toc-entry-2"><span class="sectnum">2 </span>Mathematical symbols</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#accents-and-embellishments" id="toc-entry-3"><span class="sectnum">2.1 </span>Accents and embellishments</a></p></li>
<li><p><a class="reference internal" href="#binary-operators" id="toc-entry-4"><span class="sectnum">2.2 </span>Binary operators</a></p></li>
<li><p><a class="reference internal" href="#extensible-delimiters" id="toc-entry-5"><span class="sectnum">2.3 </span>Extensible delimiters</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#pairing-delimiters" id="toc-entry-6"><span class="sectnum">2.3.1 </span>Pairing delimiters</a></p></li>
<li><p><a class="reference internal" href="#nonpairing-delimiters" id="toc-entry-7"><span class="sectnum">2.3.2 </span>Nonpairing delimiters</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#extensible-vertical-arrows" id="toc-entry-8"><span class="sectnum">2.4 </span>Extensible vertical arrows</a></p></li>
<li><p><a class="reference internal" href="#functions-named-operators" id="toc-entry-9"><span class="sectnum">2.5 </span>Functions (named operators)</a></p></li>
<li><p><a class="reference internal" href="#greek-letters" id="toc-entry-10"><span class="sectnum">2.6 </span>Greek letters</a></p></li>
<li><p><a class="reference internal" href="#letterlike-symbols" id="toc-entry-11"><span class="sectnum">2.7 </span>Letterlike symbols</a></p></li>
<li><p><a class="reference internal" href="#math-alphabets" id="toc-entry-12"><span class="sectnum">2.8 </span>Math alphabets</a></p></li>
<li><p><a class="reference internal" href="#miscellaneous-symbols" id="toc-entry-13"><span class="sectnum">2.9 </span>Miscellaneous symbols</a></p></li>
<li><p><a class="reference internal" href="#punctuation" id="toc-entry-14"><span class="sectnum">2.10 </span>Punctuation</a></p></li>
<li><p><a class="reference internal" href="#relation-symbols" id="toc-entry-15"><span class="sectnum">2.11 </span>Relation symbols</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#arrows" id="toc-entry-16"><span class="sectnum">2.11.1 </span>Arrows</a></p></li>
<li><p><a class="reference internal" href="#comparison" id="toc-entry-17"><span class="sectnum">2.11.2 </span>Comparison</a></p></li>
<li><p><a class="reference internal" href="#miscellaneous-relations" id="toc-entry-18"><span class="sectnum">2.11.3 </span>Miscellaneous relations</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#variable-sized-operators" id="toc-entry-19"><span class="sectnum">2.12 </span>Variable-sized operators</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#notations" id="toc-entry-20"><span class="sectnum">3 </span>Notations</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#top-and-bottom-embellishments" id="toc-entry-21"><span class="sectnum">3.1 </span>Top and bottom embellishments</a></p></li>
<li><p><a class="reference internal" href="#extensible-arrows" id="toc-entry-22"><span class="sectnum">3.2 </span>Extensible arrows</a></p></li>
<li><p><a class="reference internal" href="#affixing-symbols-to-other-symbols" id="toc-entry-23"><span class="sectnum">3.3 </span>Affixing symbols to other symbols</a></p></li>
<li><p><a class="reference internal" href="#matrices" id="toc-entry-24"><span class="sectnum">3.4 </span>Matrices</a></p></li>
<li><p><a class="reference internal" href="#spacing-commands" id="toc-entry-25"><span class="sectnum">3.5 </span>Spacing commands</a></p></li>
<li><p><a class="reference internal" href="#modular-arithmetic-and-modulo-operation" id="toc-entry-26"><span class="sectnum">3.6 </span>Modular arithmetic and modulo operation</a></p></li>
<li><p><a class="reference internal" href="#roots" id="toc-entry-27"><span class="sectnum">3.7 </span>Roots</a></p></li>
<li><p><a class="reference internal" href="#boxed-formulas" id="toc-entry-28"><span class="sectnum">3.8 </span>Boxed formulas</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#fractions-and-related-constructions" id="toc-entry-29"><span class="sectnum">4 </span>Fractions and related constructions</a></p></li>
<li><p><a class="reference internal" href="#delimiter-sizes" id="toc-entry-30"><span class="sectnum">5 </span>Delimiter sizes</a></p></li>
<li><p><a class="reference internal" href="#text" id="toc-entry-31"><span class="sectnum">6 </span>Text</a></p></li>
<li><p><a class="reference internal" href="#integrals-and-sums" id="toc-entry-32"><span class="sectnum">7 </span>Integrals and sums</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#altering-the-placement-of-limits" id="toc-entry-33"><span class="sectnum">7.1 </span>Altering the placement of limits</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#changing-the-size-of-elements-in-a-formula" id="toc-entry-34"><span class="sectnum">8 </span>Changing the size of elements in a formula</a></p></li>
</ul>
</nav>
<section id="inline-formulas-and-displayed-equations">
<h2><a class="toc-backref" href="#toc-entry-1" role="doc-backlink"><span class="sectnum">1 </span>Inline formulas and displayed equations</a></h2>
<p>The <strong>math role</strong> can be used for inline mathematical expressions:
<span class="docutils literal"><span class="pre">:math:`\psi(r)</span> = <span class="pre">\exp(-2r)`</span></span> will produce <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ψ</mi><mo stretchy="false" form="prefix">(</mo><mi>r</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mo>exp</mo><mo stretchy="false" form="prefix">(</mo><mo>−</mo><mn>2</mn><mi>r</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\psi(r)=\exp(-2r)</annotation></semantics></math>.
Inside the backtics you can write anything you would write between dollar
signs in a LaTeX document.  <a class="brackets" href="#math-syntax" id="footnote-reference-2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a></p>
<aside class="admonition tip">
<p class="admonition-title">Tip</p>
<p>If you put <span class="docutils literal">.. <span class="pre">default-role::</span> math</span> at the top of your
document, you can write <span class="docutils literal">`x^2`</span> instead of the longer
version: <span class="docutils literal"><span class="pre">:math:`x^2`</span></span>.  You can also introduce an
abbreviation like this <span class="docutils literal">.. role:: m(math)</span>.  That will allow
you to write <span class="docutils literal"><span class="pre">:m:`x^2`</span></span> or <span class="docutils literal"><span class="pre">`x^2`:m:</span></span>.</p>
</aside>
<p>The <strong>math directive</strong> is used for displayed equations. It corresponds to
an <span class="docutils literal">equation*</span> or <span class="docutils literal">align*</span> environment in a LaTeX document. If you
write:</p>
<pre class="literal-block">.. math:: \psi(r) = e^{-2r}</pre>
<p>you will get:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ψ</mi><mo stretchy="false" form="prefix">(</mo><mi>r</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><mn>2</mn><mi>r</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\psi(r) = e^{-2r}</annotation></semantics></math>
</div>
<p>A more complex example is the definition of the <a class="reference internal" href="#fourier-transform">Fourier transform</a>:</p>
<pre class="literal-block">.. math::
   :name: Fourier transform

   (\mathcal{F}f)(y)
    = \frac{1}{\sqrt{2\pi}^{\ n}}
      \int_{\mathbb{R}^n} f(x)\,
      e^{-\mathrm{i} y \cdot x} \,\mathrm{d} x.</pre>
<p>which is rendered as:</p>
<div id="fourier-transform">
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">(</mo><mstyle mathvariant="script"><mi>ℱ</mi></mstyle><mi>f</mi><mo stretchy="false" form="postfix">)</mo><mo stretchy="false" form="prefix">(</mo><mi>y</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mfrac><mn>1</mn><msup><msqrt><mrow><mn>2</mn><mi>π</mi></mrow></msqrt><mrow><mspace width="0.222em"></mspace><mi>n</mi></mrow></msup></mfrac><msub><mo>∫</mo><msup><mstyle mathvariant="double-struck"><mi>ℝ</mi></mstyle><mi>n</mi></msup></msub><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mspace width="0.167em"></mspace><msup><mi>e</mi><mrow><mo>−</mo><mstyle mathvariant="normal"><mi>i</mi></mstyle><mi>y</mi><mo>⋅</mo><mi>x</mi></mrow></msup><mspace width="0.167em"></mspace><mstyle mathvariant="normal"><mi>d</mi></mstyle><mi>x</mi><mi>.</mi></mrow><annotation encoding="application/x-tex">(\mathcal{F}f)(y)
   = \frac{1}{\sqrt{2\pi}^{\ n}}
     \int_{\mathbb{R}^n} f(x)\,
     e^{-\mathrm{i} y \cdot x} \,\mathrm{d} x.</annotation></semantics></math>
</div>
<p>The <span class="docutils literal">:name:</span> option puts a label on the equation that can be
linked to by <a class="reference external" href="../ref/rst/restructuredtext.html#hyperlink-references">hyperlink references</a>.</p>
<p>Displayed equations can use <span class="docutils literal">\\</span> and <span class="docutils literal">&amp;</span> for line shifts and alignments:</p>
<pre class="literal-block">.. math::

 a &amp;= (x + y)^2         &amp;  b &amp;= (x - y)^2 \\
   &amp;= x^2 + 2xy + y^2   &amp;    &amp;= x^2 - 2xy + y^2</pre>
<p>LaTeX output will wrap it in an <span class="docutils literal">align*</span> environment.
The result is:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right"><mi>a</mi></mtd><mtd columnalign="left"><mo>=</mo><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo>+</mo><mi>y</mi><msup><mo stretchy="false" form="postfix">)</mo><mn>2</mn></msup></mtd><mtd columnalign="right"><mi>b</mi></mtd><mtd columnalign="left"><mo>=</mo><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mo stretchy="false" form="postfix">)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd columnalign="right"></mtd><mtd columnalign="left"><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi><mi>y</mi><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></mtd><mtd columnalign="right"></mtd><mtd columnalign="left"><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mi>y</mi><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}
a &amp; = (x + y)^2         &amp;  b &amp; = (x - y)^2 \\
  &amp; = x^2 + 2xy + y^2   &amp;    &amp; = x^2 - 2xy + y^2\end{aligned}</annotation></semantics></math>
</div>
<p>The <span class="docutils literal">aligned</span> environment can be used as a component in a containing
expression. E.g.,</p>
<pre class="literal-block">.. math::
  \left.
    \begin{aligned}
      B' &amp; = -\partial\times E,         \\
      E' &amp; = \partial\times B - 4\pi j,
    \end{aligned}
  \right\}
  \qquad \text{Maxwell’s equations}</pre>
<p>results in</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mtable><mtr><mtd columnalign="right"><mi>B</mi><mi>′</mi></mtd><mtd columnalign="left"><mo>=</mo><mo>−</mo><mi>∂</mi><mo>×</mo><mi>E</mi></mtd></mtr><mtr><mtd columnalign="right"><mi>E</mi><mi>′</mi></mtd><mtd columnalign="left"><mo>=</mo><mi>∂</mi><mo>×</mo><mi>B</mi><mo>−</mo><mn>4</mn><mi>π</mi><mi>j</mi></mtd></mtr></mtable><mspace width="0.278em"></mspace><mo stretchy="true" form="postfix">}</mo></mrow><mspace width="2.0em"></mspace><mtext mathvariant="normal">Maxwell’s equations.</mtext></mrow><annotation encoding="application/x-tex">\left.
  \begin{aligned}
    B&#39; &amp; = -\partial\times E         \\
    E&#39; &amp; =  \partial\times B - 4\pi j
  \end{aligned}
\;\right\}
\qquad \text{Maxwell’s equations.}</annotation></semantics></math>
</div>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="math-syntax" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#footnote-reference-1">1</a>,<a role="doc-backlink" href="#footnote-reference-2">2</a>)</span>
<p>The supported LaTeX commands include AMS extensions
(see, e.g., the <a class="reference external" href="https://mirrors.ctan.org/info/short-math-guide/short-math-guide.pdf">Short Math Guide</a>). Some of the shown symbols
require the &quot;amssymb&quot; <a class="reference external" href="../../user/latex.html#latex-document-classes-and-packages">LaTeX package</a> (or another package providing
the AMS symbol macros) when exported with the &quot;latex&quot; writer.</p>
<p>The support is limited to a subset of <em>LaTeX math</em> by the conversion
required for many output formats.  For HTML, the <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a>
configuration setting (or the corresponding <span class="docutils literal"><span class="pre">--math-output</span></span> command
line option) selects between alternative output formats with different
subsets of supported elements. If a writer does not support math
typesetting, the content is inserted verbatim.</p>
</aside>
</aside>
</section>
<section id="mathematical-symbols">
<h2><a class="toc-backref" href="#toc-entry-2" role="doc-backlink"><span class="sectnum">2 </span>Mathematical symbols</a></h2>
<p>The following tables are adapted from the first edition of
&quot;The LaTeX Companion&quot; (Goossens, Mittelbach, Samarin) and the
AMS <a class="reference external" href="https://mirrors.ctan.org/info/short-math-guide/short-math-guide.pdf">Short Math Guide</a>.</p>
<section id="accents-and-embellishments">
<h3><a class="toc-backref" href="#toc-entry-3" role="doc-backlink"><span class="sectnum">2.1 </span>Accents and embellishments</a></h3>
<p>The &quot;narrow&quot; accents are intended for a single-letter base.</p>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>x</mi><mo accent="true">́</mo></mover><annotation encoding="application/x-tex">\acute{x}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\acute{x}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>t</mi><mo accent="true">̇</mo></mover><annotation encoding="application/x-tex">\dot{t}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\dot{t}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>x</mi><mo accent="true">̀</mo></mover><annotation encoding="application/x-tex">\grave{x}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\grave{x}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>x</mi><mo accent="true">⃗</mo></mover><annotation encoding="application/x-tex">\vec{x}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vec{x}</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>v</mi><mo accent="true">‾</mo></mover><annotation encoding="application/x-tex">\bar{v}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bar{v}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>t</mi><mo accent="true">̈</mo></mover><annotation encoding="application/x-tex">\ddot{t}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ddot{t}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>x</mi><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\hat{x}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\hat{x}</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>x</mi><mo accent="true">̆</mo></mover><annotation encoding="application/x-tex">\breve{x}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\breve{x}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>t</mi><mo accent="true">⃛</mo></mover><annotation encoding="application/x-tex">\dddot{t}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\dddot{t}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>x</mi><mo accent="true">̊</mo></mover><annotation encoding="application/x-tex">\mathring{x}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\mathring{x}</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>x</mi><mo accent="true">̌</mo></mover><annotation encoding="application/x-tex">\check{x}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\check{x}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>t</mi><mo accent="true">⃜</mo></mover><annotation encoding="application/x-tex">\ddddot{t}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ddddot{t}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>n</mi><mo accent="true">̃</mo></mover><annotation encoding="application/x-tex">\tilde{n}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\tilde{n}</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p>When adding an accent to an i or j in math, dotless variants can be
obtained with <span class="docutils literal">\imath</span> and <span class="docutils literal">\jmath</span>: <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mo>ı</mo><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\hat \imath</annotation></semantics></math>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mo>ȷ</mo><mo accent="true">⃗</mo></mover><annotation encoding="application/x-tex">\vec{\jmath}</annotation></semantics></math>.</p>
<p>For embellishments that span multiple symbols, use:</p>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">̃</mo></mover><annotation encoding="application/x-tex">\widetilde{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\widetilde{gbi}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\widehat{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\widehat{gbi}</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">¯</mo></mover><annotation encoding="application/x-tex">\overline{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\overline{gbi}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><munder><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">_</mo></munder><annotation encoding="application/x-tex">\underline{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\underline{gbi}</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">⏞</mo></mover><annotation encoding="application/x-tex">\overbrace{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\overbrace{gbi}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><munder><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">⏟</mo></munder><annotation encoding="application/x-tex">\underbrace{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\underbrace{gbi}</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">⃖</mo></mover><annotation encoding="application/x-tex">\overleftarrow{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\overleftarrow{gbi}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">⃮</mo></mover><annotation encoding="application/x-tex">\underleftarrow{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\underleftarrow{gbi}</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">⃗</mo></mover><annotation encoding="application/x-tex">\overrightarrow{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\overrightarrow{gbi}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">⃯</mo></mover><annotation encoding="application/x-tex">\underrightarrow{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\underrightarrow{gbi}</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>g</mi><mi>b</mi><mi>i</mi></mrow><mo accent="true">⃡</mo></mover><annotation encoding="application/x-tex">\overleftrightarrow{gbi}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\overleftrightarrow{gbi}</span></p></td>
<td><p><span class="math problematic m">\underleftrightarrow{gbi}</span></p></td>
<td><p><span class="docutils literal">\underleftrightarrow{gbi}</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 167)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\underleftrightarrow{gbi}', rendering as TeX:</p>
<pre class="literal-block">  underleftrightarrow{gbi}
                     ^</pre>
<p class="pre-wrap">  unexpected &quot;{&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</section>
<section id="binary-operators">
<h3><a class="toc-backref" href="#toc-entry-4" role="doc-backlink"><span class="sectnum">2.2 </span>Binary operators</a></h3>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>*</mo><annotation encoding="application/x-tex">*</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">*</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊛</mo><annotation encoding="application/x-tex">\circledast</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\circledast</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊖</mo><annotation encoding="application/x-tex">\ominus</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ominus</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>+</mo><annotation encoding="application/x-tex">+</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">+</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>◎</mi><annotation encoding="application/x-tex">\circledcirc</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\circledcirc</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊕</mo><annotation encoding="application/x-tex">\oplus</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\oplus</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>−</mo><annotation encoding="application/x-tex">-</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">-</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊝</mo><annotation encoding="application/x-tex">\circleddash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\circleddash</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊘</mo><annotation encoding="application/x-tex">\oslash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\oslash</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>:</mo><annotation encoding="application/x-tex">:</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">:</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∪</mo><annotation encoding="application/x-tex">\cup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\cup</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊗</mo><annotation encoding="application/x-tex">\otimes</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\otimes</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋒</mo><annotation encoding="application/x-tex">\Cap</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Cap</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋎</mo><annotation encoding="application/x-tex">\curlyvee</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\curlyvee</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>±</mo><annotation encoding="application/x-tex">\pm</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\pm</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋓</mo><annotation encoding="application/x-tex">\Cup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Cup</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋏</mo><annotation encoding="application/x-tex">\curlywedge</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\curlywedge</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋌</mo><annotation encoding="application/x-tex">\rightthreetimes</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightthreetimes</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∐</mo><annotation encoding="application/x-tex">\amalg</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\amalg</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>†</mo><annotation encoding="application/x-tex">\dagger</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\dagger</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋊</mo><annotation encoding="application/x-tex">\rtimes</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rtimes</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>*</mo><annotation encoding="application/x-tex">\ast</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ast</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>‡</mo><annotation encoding="application/x-tex">\ddagger</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ddagger</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>\</mo><annotation encoding="application/x-tex">\setminus</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\setminus</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>○</mo><annotation encoding="application/x-tex">\bigcirc</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bigcirc</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋄</mo><annotation encoding="application/x-tex">\diamond</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\diamond</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∖</mo><annotation encoding="application/x-tex">\smallsetminus</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\smallsetminus</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>▽</mo><annotation encoding="application/x-tex">\bigtriangledown</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bigtriangledown</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>÷</mo><annotation encoding="application/x-tex">\div</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\div</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊓</mo><annotation encoding="application/x-tex">\sqcap</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sqcap</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>△</mo><annotation encoding="application/x-tex">\bigtriangleup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bigtriangleup</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋇</mo><annotation encoding="application/x-tex">\divideontimes</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\divideontimes</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊔</mo><annotation encoding="application/x-tex">\sqcup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sqcup</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊡</mo><annotation encoding="application/x-tex">\boxdot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\boxdot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∔</mo><annotation encoding="application/x-tex">\dotplus</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\dotplus</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋆</mo><annotation encoding="application/x-tex">\star</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\star</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊟</mo><annotation encoding="application/x-tex">\boxminus</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\boxminus</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⌆</mo><annotation encoding="application/x-tex">\doublebarwedge</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\doublebarwedge</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>×</mo><annotation encoding="application/x-tex">\times</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\times</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊞</mo><annotation encoding="application/x-tex">\boxplus</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\boxplus</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋗</mo><annotation encoding="application/x-tex">\gtrdot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gtrdot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊲</mo><annotation encoding="application/x-tex">\triangleleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\triangleleft</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊠</mo><annotation encoding="application/x-tex">\boxtimes</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\boxtimes</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊺</mo><annotation encoding="application/x-tex">\intercal</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\intercal</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊳</mo><annotation encoding="application/x-tex">\triangleright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\triangleright</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>•</mo><annotation encoding="application/x-tex">\bullet</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bullet</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋋</mo><annotation encoding="application/x-tex">\leftthreetimes</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftthreetimes</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊎</mo><annotation encoding="application/x-tex">\uplus</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\uplus</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∩</mo><annotation encoding="application/x-tex">\cap</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\cap</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋖</mo><annotation encoding="application/x-tex">\lessdot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lessdot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∨</mo><annotation encoding="application/x-tex">\vee</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vee</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋅</mo><annotation encoding="application/x-tex">\cdot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\cdot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋉</mo><annotation encoding="application/x-tex">\ltimes</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ltimes</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊻</mo><annotation encoding="application/x-tex">\veebar</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\veebar</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⬝</mi><annotation encoding="application/x-tex">\centerdot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\centerdot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∓</mo><annotation encoding="application/x-tex">\mp</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\mp</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∧</mo><annotation encoding="application/x-tex">\wedge</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\wedge</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∘</mo><annotation encoding="application/x-tex">\circ</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\circ</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊙</mo><annotation encoding="application/x-tex">\odot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\odot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>≀</mi><annotation encoding="application/x-tex">\wr</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\wr</span></p></td>
</tr>
</tbody>
</table>
</section>
<section id="extensible-delimiters">
<h3><a class="toc-backref" href="#toc-entry-5" role="doc-backlink"><span class="sectnum">2.3 </span>Extensible delimiters</a></h3>
<p>Unless you indicate otherwise, delimiters in math formulas remain at the
standard size regardless of the height of the enclosed material. To get
adaptable sizes, use <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> prefixes, for example
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi><mo stretchy="false" form="prefix">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>Y</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>X</mi><mo>=</mo><msup><mi>h</mi><mrow><mo stretchy="false" form="prefix">[</mo><mi>X</mi><mo stretchy="false" form="postfix">]</mo></mrow></msup><mo stretchy="false" form="prefix">(</mo><mi>Y</mi><mo stretchy="false" form="postfix">)</mo><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">g(A,B,Y) = f \left(A,B,X=h^{[X]}(Y)\right)</annotation></semantics></math> or</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mo stretchy="true" form="prefix">(</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><mi>n</mi></msup></mrow><annotation encoding="application/x-tex">a_n = \left(\frac{1}{2}\right)^n</annotation></semantics></math>
</div>
<p>Use <span class="docutils literal">.</span> for &quot;empty&quot; delimiters:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><msubsup><mrow><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mi>n</mi></mrow></mfrac><mspace width="0.167em"></mspace><mo stretchy="true" form="postfix">|</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mi>∞</mi></msubsup></mrow><annotation encoding="application/x-tex">A = \left . \frac{1}{1-n}\, \right |_{n=0}^\infty</annotation></semantics></math>
</div>
<p>See also the commands for fixed <a class="reference internal" href="#delimiter-sizes">delimiter sizes</a> below.</p>
<p>The following symbols extend when used with <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span>:</p>
<section id="pairing-delimiters">
<h4><a class="toc-backref" href="#toc-entry-6" role="doc-backlink"><span class="sectnum">2.3.1 </span>Pairing delimiters</a></h4>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">(</mo><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">( )</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">( )</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">⟨</mo><mo stretchy="false" form="postfix">⟩</mo></mrow><annotation encoding="application/x-tex">\langle \rangle</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\langle \rangle</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">[</mo><mo stretchy="false" form="postfix">]</mo></mrow><annotation encoding="application/x-tex">[ ]</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">[ ]</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">⌈</mo><mo stretchy="false" form="postfix">⌉</mo></mrow><annotation encoding="application/x-tex">\lceil  \rceil</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lceil \rceil</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">{</mo><mo stretchy="false" form="postfix">}</mo></mrow><annotation encoding="application/x-tex">\{ \}</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\{ \}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">⌊</mo><mo stretchy="false" form="postfix">⌋</mo></mrow><annotation encoding="application/x-tex">\lfloor \rfloor</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lfloor \rfloor</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">|</mo><mo stretchy="false" form="postfix">|</mo></mrow><annotation encoding="application/x-tex">\lvert \rvert</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lvert \rvert</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">⟮</mo><mo stretchy="false" form="postfix">⟯</mo></mrow><annotation encoding="application/x-tex">\lgroup \rgroup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lgroup \rgroup</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">∥</mo><mo stretchy="false" form="postfix">∥</mo></mrow><annotation encoding="application/x-tex">\lVert \rVert</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lVert \rVert</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>⎰</mi><mi>⎱</mi></mrow><annotation encoding="application/x-tex">\lmoustache \rmoustache</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lmoustache \rmoustache</span></p></td>
</tr>
</tbody>
</table>
</section>
<section id="nonpairing-delimiters">
<h4><a class="toc-backref" href="#toc-entry-7" role="doc-backlink"><span class="sectnum">2.3.2 </span>Nonpairing delimiters</a></h4>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo stretchy="false" form="prefix">|</mo><annotation encoding="application/x-tex">|</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">|</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo stretchy="false" form="postfix">|</mo><annotation encoding="application/x-tex">\vert</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vert</span></p></td>
<td><p><span class="math problematic m">\arrowvert</span></p></td>
<td><p><span class="docutils literal">\arrowvert</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo stretchy="false" form="postfix">∥</mo><annotation encoding="application/x-tex">\|</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\|</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo stretchy="false" form="postfix">‖</mo><annotation encoding="application/x-tex">\Vert</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Vert</span></p></td>
<td><p><span class="math problematic m">\Arrowvert</span></p></td>
<td><p><span class="docutils literal">\Arrowvert</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>/</mi><annotation encoding="application/x-tex">/</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">/</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∖</mo><annotation encoding="application/x-tex">\backslash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\backslash</span></p></td>
<td><p><span class="math problematic m">\bracevert</span></p></td>
<td><p><span class="docutils literal">\bracevert</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 234)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\arrowvert', rendering as TeX:</p>
<pre class="literal-block">  \arrowvert
            ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 235)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\Arrowvert', rendering as TeX:</p>
<pre class="literal-block">  \Arrowvert
            ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 236)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\bracevert', rendering as TeX:</p>
<pre class="literal-block">  \bracevert
            ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>The use of <span class="docutils literal">|</span> and <span class="docutils literal">\|</span> for pairs of vertical bars may produce
incorrect spacing, e.g., <span class="docutils literal"><span class="pre">|k|=|-k|</span></span> produces <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">|</mo><mi>k</mi><mo stretchy="false" form="prefix">|</mo><mo>=</mo><mo stretchy="false" form="prefix">|</mo><mo>−</mo><mi>k</mi><mo stretchy="false" form="prefix">|</mo></mrow><annotation encoding="application/x-tex">|k| = |-k|</annotation></semantics></math> and
<span class="docutils literal">|\sin(x)|</span> produces <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">|</mo><mo>sin</mo><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mo stretchy="false" form="prefix">|</mo></mrow><annotation encoding="application/x-tex">|\sin(x)|</annotation></semantics></math>. The pairing delimiters, e.g.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">|</mo><mo>−</mo><mi>k</mi><mo stretchy="false" form="postfix">|</mo></mrow><annotation encoding="application/x-tex">\lvert -k\rvert</annotation></semantics></math> and <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">|</mo><mo>sin</mo><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mo stretchy="false" form="postfix">|</mo></mrow><annotation encoding="application/x-tex">\lvert\sin(x)\rvert</annotation></semantics></math>, prevent this problem.</p>
</section>
</section>
<section id="extensible-vertical-arrows">
<h3><a class="toc-backref" href="#toc-entry-8" role="doc-backlink"><span class="sectnum">2.4 </span>Extensible vertical arrows</a></h3>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↑</mo><annotation encoding="application/x-tex">\uparrow</annotation></semantics></math>     <span class="docutils literal">\uparrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇑</mo><annotation encoding="application/x-tex">\Uparrow</annotation></semantics></math>     <span class="docutils literal">\Uparrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↓</mo><annotation encoding="application/x-tex">\downarrow</annotation></semantics></math>   <span class="docutils literal">\downarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇓</mo><annotation encoding="application/x-tex">\Downarrow</annotation></semantics></math>   <span class="docutils literal">\Downarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↕</mo><annotation encoding="application/x-tex">\updownarrow</annotation></semantics></math> <span class="docutils literal">\updownarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇕</mo><annotation encoding="application/x-tex">\Updownarrow</annotation></semantics></math> <span class="docutils literal">\Updownarrow</span></p></td>
</tr>
</tbody>
</table>
</section>
<section id="functions-named-operators">
<h3><a class="toc-backref" href="#toc-entry-9" role="doc-backlink"><span class="sectnum">2.5 </span>Functions (named operators)</a></h3>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>arccos</mo><annotation encoding="application/x-tex">\arccos</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\arccos</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>gcd</mo><annotation encoding="application/x-tex">\gcd</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gcd</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>Pr</mo><annotation encoding="application/x-tex">\Pr</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Pr</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>arcsin</mo><annotation encoding="application/x-tex">\arcsin</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\arcsin</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>hom</mo><annotation encoding="application/x-tex">\hom</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\hom</span></p></td>
<td><p><span class="math problematic m">\projlim</span></p></td>
<td><p><span class="docutils literal">\projlim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>arctan</mo><annotation encoding="application/x-tex">\arctan</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\arctan</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>inf</mo><annotation encoding="application/x-tex">\inf</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\inf</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>sec</mo><annotation encoding="application/x-tex">\sec</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sec</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>arg</mo><annotation encoding="application/x-tex">\arg</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\arg</span></p></td>
<td><p><span class="math problematic m">\injlim</span></p></td>
<td><p><span class="docutils literal">\injlim</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>sin</mo><annotation encoding="application/x-tex">\sin</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sin</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>cos</mo><annotation encoding="application/x-tex">\cos</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\cos</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ker</mo><annotation encoding="application/x-tex">\ker</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ker</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>sinh</mo><annotation encoding="application/x-tex">\sinh</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sinh</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>cosh</mo><annotation encoding="application/x-tex">\cosh</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\cosh</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>lg</mo><annotation encoding="application/x-tex">\lg</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lg</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>sup</mo><annotation encoding="application/x-tex">\sup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sup</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>cot</mo><annotation encoding="application/x-tex">\cot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\cot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>lim</mo><annotation encoding="application/x-tex">\lim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lim</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>tan</mo><annotation encoding="application/x-tex">\tan</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\tan</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>coth</mo><annotation encoding="application/x-tex">\coth</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\coth</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>liminf</mo><annotation encoding="application/x-tex">\liminf</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\liminf</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>tanh</mo><annotation encoding="application/x-tex">\tanh</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\tanh</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>csc</mo><annotation encoding="application/x-tex">\csc</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\csc</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>limsup</mo><annotation encoding="application/x-tex">\limsup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\limsup</span></p></td>
<td><p><span class="math problematic m">\varlimsup</span></p></td>
<td><p><span class="docutils literal">\varlimsup</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>deg</mo><annotation encoding="application/x-tex">\deg</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\deg</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ln</mo><annotation encoding="application/x-tex">\ln</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ln</span></p></td>
<td><p><span class="math problematic m">\varliminf</span></p></td>
<td><p><span class="docutils literal">\varliminf</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>det</mo><annotation encoding="application/x-tex">\det</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\det</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>log</mo><annotation encoding="application/x-tex">\log</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\log</span></p></td>
<td><p><span class="math problematic m">\varprojlim</span></p></td>
<td><p><span class="docutils literal">\varprojlim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>dim</mo><annotation encoding="application/x-tex">\dim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\dim</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>max</mo><annotation encoding="application/x-tex">\max</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\max</span></p></td>
<td><p><span class="math problematic m">\varinjlim</span></p></td>
<td><p><span class="docutils literal">\varinjlim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>exp</mo><annotation encoding="application/x-tex">\exp</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\exp</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>min</mo><annotation encoding="application/x-tex">\min</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\min</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 262)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\projlim', rendering as TeX:</p>
<pre class="literal-block">  \projlim
          ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 264)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\injlim', rendering as TeX:</p>
<pre class="literal-block">  \injlim
         ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 269)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\varlimsup', rendering as TeX:</p>
<pre class="literal-block">  \varlimsup
            ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 270)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\varliminf', rendering as TeX:</p>
<pre class="literal-block">  \varliminf
            ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 271)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\varprojlim', rendering as TeX:</p>
<pre class="literal-block">  \varprojlim
             ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 272)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\varinjlim', rendering as TeX:</p>
<pre class="literal-block">  \varinjlim
            ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>Named operators outside the above list can be typeset with
<span class="docutils literal">\operatorname{name}</span>, e.g.</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>sgn</mo><mo stretchy="false" form="prefix">(</mo><mo>−</mo><mn>3</mn><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mo>−</mo><mn>1</mn><mi>.</mi></mrow><annotation encoding="application/x-tex">\operatorname{sgn}(-3) = -1.</annotation></semantics></math>
</div>
<!-- TODO: \operatorname* for function name with limits. -->
<p>The <span class="docutils literal">\DeclareMathOperator</span> command can only be used in the
<a class="reference external" href="latex.html#latex-preamble">LaTeX preamble</a>.</p>
</section>
<section id="greek-letters">
<h3><a class="toc-backref" href="#toc-entry-10" role="doc-backlink"><span class="sectnum">2.6 </span>Greek letters</a></h3>
<p>Greek letters that have Latin look-alikes are rarely used in math
formulas and not supported by LaTeX.</p>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Γ</mi><annotation encoding="application/x-tex">\Gamma</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Gamma</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\alpha</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>μ</mi><annotation encoding="application/x-tex">\mu</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\mu</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ω</mi><annotation encoding="application/x-tex">\omega</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\omega</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Δ</mi><annotation encoding="application/x-tex">\Delta</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Delta</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>β</mi><annotation encoding="application/x-tex">\beta</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\beta</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ν</mi><annotation encoding="application/x-tex">\nu</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nu</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ϝ</mo><annotation encoding="application/x-tex">\digamma</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\digamma</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Λ</mi><annotation encoding="application/x-tex">\Lambda</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Lambda</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>γ</mi><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gamma</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ξ</mi><annotation encoding="application/x-tex">\xi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\xi</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ε</mi><annotation encoding="application/x-tex">\varepsilon</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\varepsilon</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Φ</mi><annotation encoding="application/x-tex">\Phi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Phi</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>δ</mi><annotation encoding="application/x-tex">\delta</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\delta</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>π</mi><annotation encoding="application/x-tex">\pi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\pi</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>𝜘</mo><annotation encoding="application/x-tex">\varkappa</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\varkappa</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Π</mi><annotation encoding="application/x-tex">\Pi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Pi</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϵ</mi><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\epsilon</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ρ</mi><annotation encoding="application/x-tex">\rho</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rho</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>φ</mi><annotation encoding="application/x-tex">\varphi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\varphi</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Ψ</mi><annotation encoding="application/x-tex">\Psi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Psi</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ζ</mi><annotation encoding="application/x-tex">\zeta</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\zeta</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>σ</mi><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sigma</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ϖ</mo><annotation encoding="application/x-tex">\varpi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\varpi</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Σ</mi><annotation encoding="application/x-tex">\Sigma</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Sigma</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>η</mi><annotation encoding="application/x-tex">\eta</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\eta</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>τ</mi><annotation encoding="application/x-tex">\tau</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\tau</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>𝜚</mo><annotation encoding="application/x-tex">\varrho</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\varrho</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Θ</mi><annotation encoding="application/x-tex">\Theta</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Theta</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>θ</mi><annotation encoding="application/x-tex">\theta</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\theta</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>υ</mi><annotation encoding="application/x-tex">\upsilon</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\upsilon</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ς</mo><annotation encoding="application/x-tex">\varsigma</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\varsigma</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Υ</mi><annotation encoding="application/x-tex">\Upsilon</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Upsilon</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ι</mi><annotation encoding="application/x-tex">\iota</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\iota</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϕ</mi><annotation encoding="application/x-tex">\phi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\phi</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϑ</mi><annotation encoding="application/x-tex">\vartheta</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vartheta</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Ξ</mi><annotation encoding="application/x-tex">\Xi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Xi</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>κ</mi><annotation encoding="application/x-tex">\kappa</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\kappa</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>χ</mi><annotation encoding="application/x-tex">\chi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\chi</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Ω</mi><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Omega</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>λ</mi><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lambda</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ψ</mi><annotation encoding="application/x-tex">\psi</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\psi</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p>In LaTeX, the default font for capital Greek letters is upright/roman.
<em>Italic</em> capital Greek letters can be obtained by loading a <a class="reference external" href="https://mirrors.ctan.org/macros/latex/contrib/isomath/isomath.html#table-2">package
providing the &quot;ISO&quot; math style</a>. They are used by default in MathML.</p>
<p>Individual Greek italic capitals can also be achieved preceding the
letter name with <span class="docutils literal">var</span> like <span class="docutils literal">\varPhi</span>:
<span class="math problematic m">\varGamma\ \varDelta\ \varLambda\ \varPhi\ \varPi\ \varPsi\ \varSigma\
\varTheta\ \varUpsilon\ \varXi\ \varOmega</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 315)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\varGamma\ \varDelta\ \varLambda\ \varPhi\ \varPi\ \varPsi\ \varSigma\</p>
<pre class="literal-block">  \varTheta\ \varUpsilon\ \varXi\ \varOmega', rendering as TeX:
  \varGamma\ \varDelta\ \varLambda\ \varPh</pre>
<p class="pre-wrap">           ^
  unexpected &quot;\\&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</section>
<section id="letterlike-symbols">
<h3><a class="toc-backref" href="#toc-entry-11" role="doc-backlink"><span class="sectnum">2.7 </span>Letterlike symbols</a></h3>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∀</mo><annotation encoding="application/x-tex">\forall</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\forall</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℵ</mi><annotation encoding="application/x-tex">\aleph</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\aleph</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℏ</mi><annotation encoding="application/x-tex">\hbar</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\hbar</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℓ</mi><annotation encoding="application/x-tex">\ell</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ell</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∁</mi><annotation encoding="application/x-tex">\complement</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\complement</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ℶ</mo><annotation encoding="application/x-tex">\beth</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\beth</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ℏ</mo><annotation encoding="application/x-tex">\hslash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\hslash</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>℘</mi><annotation encoding="application/x-tex">\wp</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\wp</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∃</mo><annotation encoding="application/x-tex">\exists</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\exists</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ℷ</mo><annotation encoding="application/x-tex">\gimel</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gimel</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℑ</mi><annotation encoding="application/x-tex">\Im</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Im</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℜ</mi><annotation encoding="application/x-tex">\Re</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Re</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Ⅎ</mi><annotation encoding="application/x-tex">\Finv</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Finv</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ℸ</mo><annotation encoding="application/x-tex">\daleth</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\daleth</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ı</mo><annotation encoding="application/x-tex">\imath</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\imath</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>®</mi><annotation encoding="application/x-tex">\circledR</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\circledR</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⅁</mi><annotation encoding="application/x-tex">\Game</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Game</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∂</mi><annotation encoding="application/x-tex">\partial</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\partial</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ȷ</mo><annotation encoding="application/x-tex">\jmath</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\jmath</span></p></td>
<td><p><span class="math problematic m">\circledS</span></p></td>
<td><p><span class="docutils literal">\circledS</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>℧</mi><annotation encoding="application/x-tex">\mho</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\mho</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ð</mo><annotation encoding="application/x-tex">\eth</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\eth</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>𝕜</mo><annotation encoding="application/x-tex">\Bbbk</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Bbbk</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 333)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\circledS', rendering as TeX:</p>
<pre class="literal-block">  \circledS
           ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</section>
<section id="math-alphabets">
<span id="math-alphabet"></span><h3><a class="toc-backref" href="#toc-entry-12" role="doc-backlink"><span class="sectnum">2.8 </span>Math alphabets</a></h3>
<p>The TeX <em>math alphabet</em> macros are intended for mathematical variables
where style variations are important semantically.
They style letters and numbers with a combination of font attributes
(shape, weight, family) --- non-alphanumerical symbols, function names,
and mathematical text are left unchanged.</p>
<p>MathML uses the <em>mathvariant</em> <a class="reference external" href="https://www.w3.org/TR/mathml4/#presm_commatt">style attribute</a> or pre-styled characters
from the <a class="reference external" href="https://en.wikipedia.org/wiki/Mathematical_Alphanumeric_Symbols">Mathematical Alphanumeric Symbols</a> Unicode block.</p>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\mathrm</span></p></td>
<td><p><span class="docutils literal">s_\mathrm{out}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>s</mi><mstyle mathvariant="normal"><mi>o</mi><mi>u</mi><mi>t</mi></mstyle></msub><annotation encoding="application/x-tex">s_\mathrm{out}</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathbf</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\mathbf{r}^2=x^2+y^2</span></span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mstyle mathvariant="bold"><mi>𝐫</mi></mstyle><mn>2</mn></msup><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\mathbf{r}^2=x^2+y^2</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathit</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\mathit{\sin\Gamma}</span></span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="italic"><mo>sin</mo><mi>𝛤</mi></mstyle><annotation encoding="application/x-tex">\mathit{\sin\Gamma}</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathcal</span></p></td>
<td><p><span class="docutils literal">\mathcal{F}f(x)</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathvariant="script"><mi>ℱ</mi></mstyle><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\mathcal{F}f(x)</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathbb</span></p></td>
<td><p><span class="docutils literal">\mathbb{R \subset C}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="double-struck"><mi>ℝ</mi><mo>⊂</mo><mi>ℂ</mi></mstyle><annotation encoding="application/x-tex">\mathbb{R \subset C}</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathfrak</span></p></td>
<td><p><span class="docutils literal">\mathfrak{a+b}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="fraktur"><mi>𝔞</mi><mo>+</mo><mi>𝔟</mi></mstyle><annotation encoding="application/x-tex">\mathfrak{a+b}</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathsf</span></p></td>
<td><p><span class="docutils literal">\mathsf x</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="sans-serif"><mi>𝗑</mi></mstyle><annotation encoding="application/x-tex">\mathsf x</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathtt</span></p></td>
<td><p><span class="docutils literal">\mathtt{0.12}</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="monospace"><mn>0.12</mn></mstyle><annotation encoding="application/x-tex">\mathtt{0.12}</annotation></semantics></math></p></td>
</tr>
</tbody>
</table>
<p>The set of characters in a given &quot;math alphabet&quot; varies.
LaTeX may produce garbage for unsupported characters.
Additional math alphabets are defined in LaTeX packages, e.g.,</p>
<ul class="simple">
<li><p><span class="docutils literal">\mathbfit</span> from <a class="reference external" href="https://www.ctan.org/pkg/isomath">isomath</a> allows vector symbols in line with the
International Standard <a class="citation-reference" href="#iso-80000-2" id="citation-reference-1" role="doc-biblioref">[ISO-80000-2]</a>.
E.g., <span class="docutils literal"><span class="pre">\mathbfit{r}^2=x^2+y^2</span></span> becomes <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mstyle mathvariant="bold-italic"><mi>𝒓</mi></mstyle><mn>2</mn></msup><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\mathbfit{r}^2=x^2+y^2</annotation></semantics></math>.</p></li>
<li><p>Several packages, e.g. <a class="reference external" href="https://www.ctan.org/pkg/mathrsfs">mathrsfs</a>, define <span class="docutils literal">\mathscr</span> that selects a
differently shaped &quot;script&quot; alphabet.</p></li>
</ul>
<p>The listing below shows the characters supported by Unicode and
Docutils with <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> MathML. <a class="brackets" href="#italic-digits" id="footnote-reference-3" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a></p>
<dl class="simple">
<dt>default:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>D</mi><mi>E</mi><mi>F</mi><mi>G</mi><mi>H</mi><mi>I</mi><mi>J</mi><mi>K</mi><mi>L</mi><mi>M</mi><mi>N</mi><mi>O</mi><mi>P</mi><mi>Q</mi><mi>R</mi><mi>S</mi><mi>T</mi><mi>U</mi><mi>V</mi><mi>W</mi><mi>X</mi><mi>Y</mi><mi>Z</mi><mspace width="0.222em"></mspace><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi><mi>f</mi><mi>g</mi><mi>h</mi><mi>i</mi><mi>j</mi><mi>k</mi><mi>l</mi><mi>m</mi><mi>n</mi><mi>o</mi><mi>p</mi><mi>q</mi><mi>r</mi><mi>s</mi><mi>t</mi><mi>u</mi><mi>v</mi><mi>w</mi><mi>x</mi><mi>y</mi><mi>z</mi><mspace width="0.222em"></mspace><mo>ı</mo><mo>ȷ</mo></mrow><annotation encoding="application/x-tex">{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz\ \imath \jmath}</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Γ</mi><mi>Δ</mi><mi>Θ</mi><mi>Λ</mi><mi>Ξ</mi><mi>Π</mi><mi>Σ</mi><mi>Υ</mi><mi>Φ</mi><mi>Ψ</mi><mi>Ω</mi><mspace width="0.222em"></mspace><mi>α</mi><mi>β</mi><mi>γ</mi><mi>δ</mi><mi>ε</mi><mi>ζ</mi><mi>η</mi><mi>θ</mi><mi>ι</mi><mi>κ</mi><mi>λ</mi><mi>μ</mi><mi>ν</mi><mi>ξ</mi><mi>π</mi><mi>ρ</mi><mo>ς</mo><mi>σ</mi><mi>τ</mi><mi>υ</mi><mi>φ</mi><mi>χ</mi><mi>ψ</mi><mi>ω</mi><mspace width="0.222em"></mspace><mi>ϵ</mi><mi>ϑ</mi><mi>ϕ</mi><mo>𝜘</mo><mo>𝜚</mo><mo>ϖ</mo><mi>Ϝ</mi><mo>ϝ</mo><mspace width="0.222em"></mspace><mi>∂</mi><mi>∇</mi></mrow><annotation encoding="application/x-tex">{\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega \ \alpha \beta \gamma \delta \varepsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \pi \rho \varsigma \sigma \tau \upsilon \varphi \chi \psi \omega \ \epsilon \vartheta \phi \varkappa \varrho \varpi Ϝ\digamma \ \partial\nabla }</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>0123456789</mn><annotation encoding="application/x-tex">{0123456789}</annotation></semantics></math></p>
</dd>
<dt>mathrm:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="normal"><mi>A</mi><mi>B</mi><mi>C</mi><mi>D</mi><mi>E</mi><mi>F</mi><mi>G</mi><mi>H</mi><mi>I</mi><mi>J</mi><mi>K</mi><mi>L</mi><mi>M</mi><mi>N</mi><mi>O</mi><mi>P</mi><mi>Q</mi><mi>R</mi><mi>S</mi><mi>T</mi><mi>U</mi><mi>V</mi><mi>W</mi><mi>X</mi><mi>Y</mi><mi>Z</mi><mspace width="0.222em"></mspace><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi><mi>e</mi><mi>f</mi><mi>g</mi><mi>h</mi><mi>i</mi><mi>j</mi><mi>k</mi><mi>l</mi><mi>m</mi><mi>n</mi><mi>o</mi><mi>p</mi><mi>q</mi><mi>r</mi><mi>s</mi><mi>t</mi><mi>u</mi><mi>v</mi><mi>w</mi><mi>x</mi><mi>y</mi><mi>z</mi><mspace width="0.222em"></mspace><mo>ı</mo><mo>ȷ</mo></mstyle><annotation encoding="application/x-tex">\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz\ \imath \jmath}</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="normal"><mi>Γ</mi><mi>Δ</mi><mi>Θ</mi><mi>Λ</mi><mi>Ξ</mi><mi>Π</mi><mi>Σ</mi><mi>Υ</mi><mi>Φ</mi><mi>Ψ</mi><mi>Ω</mi><mspace width="0.222em"></mspace><mi>α</mi><mi>β</mi><mi>γ</mi><mi>δ</mi><mi>ε</mi><mi>ζ</mi><mi>η</mi><mi>θ</mi><mi>ι</mi><mi>κ</mi><mi>λ</mi><mi>μ</mi><mi>ν</mi><mi>ξ</mi><mi>π</mi><mi>ρ</mi><mo>ς</mo><mi>σ</mi><mi>τ</mi><mi>υ</mi><mi>φ</mi><mi>χ</mi><mi>ψ</mi><mi>ω</mi><mspace width="0.222em"></mspace><mi>ϵ</mi><mi>ϑ</mi><mi>ϕ</mi><mo>𝜘</mo><mo>𝜚</mo><mo>ϖ</mo><mi>Ϝ</mi><mo>ϝ</mo><mspace width="0.222em"></mspace><mi>∂</mi><mi>∇</mi></mstyle><annotation encoding="application/x-tex">\mathrm{\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega \ \alpha \beta \gamma \delta \varepsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \pi \rho \varsigma \sigma \tau \upsilon \varphi \chi \psi \omega \ \epsilon \vartheta \phi \varkappa \varrho \varpi Ϝ\digamma \ \partial\nabla }</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="normal"><mn>0123456789</mn></mstyle><annotation encoding="application/x-tex">\mathrm{0123456789}</annotation></semantics></math></p>
</dd>
<dt>mathbf:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="bold"><mi>𝐀</mi><mi>𝐁</mi><mi>𝐂</mi><mi>𝐃</mi><mi>𝐄</mi><mi>𝐅</mi><mi>𝐆</mi><mi>𝐇</mi><mi>𝐈</mi><mi>𝐉</mi><mi>𝐊</mi><mi>𝐋</mi><mi>𝐌</mi><mi>𝐍</mi><mi>𝐎</mi><mi>𝐏</mi><mi>𝐐</mi><mi>𝐑</mi><mi>𝐒</mi><mi>𝐓</mi><mi>𝐔</mi><mi>𝐕</mi><mi>𝐖</mi><mi>𝐗</mi><mi>𝐘</mi><mi>𝐙</mi><mspace width="0.222em"></mspace><mi>𝐚</mi><mi>𝐛</mi><mi>𝐜</mi><mi>𝐝</mi><mi>𝐞</mi><mi>𝐟</mi><mi>𝐠</mi><mi>𝐡</mi><mi>𝐢</mi><mi>𝐣</mi><mi>𝐤</mi><mi>𝐥</mi><mi>𝐦</mi><mi>𝐧</mi><mi>𝐨</mi><mi>𝐩</mi><mi>𝐪</mi><mi>𝐫</mi><mi>𝐬</mi><mi>𝐭</mi><mi>𝐮</mi><mi>𝐯</mi><mi>𝐰</mi><mi>𝐱</mi><mi>𝐲</mi><mi>𝐳</mi></mstyle><annotation encoding="application/x-tex">\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="bold"><mi>𝚪</mi><mi>𝚫</mi><mi>𝚯</mi><mi>𝚲</mi><mi>𝚵</mi><mi>𝚷</mi><mi>𝚺</mi><mi>𝚼</mi><mi>𝚽</mi><mi>𝚿</mi><mi>𝛀</mi><mspace width="0.222em"></mspace><mi>𝛂</mi><mi>𝛃</mi><mi>𝛄</mi><mi>𝛅</mi><mi>𝛆</mi><mi>𝛇</mi><mi>𝛈</mi><mi>𝛉</mi><mi>𝛊</mi><mi>𝛋</mi><mi>𝛌</mi><mi>𝛍</mi><mi>𝛎</mi><mi>𝛏</mi><mi>𝛑</mi><mi>𝛒</mi><mo>ς</mo><mi>𝛔</mi><mi>𝛕</mi><mi>𝛖</mi><mi>𝛗</mi><mi>𝛘</mi><mi>𝛙</mi><mi>𝛚</mi><mspace width="0.222em"></mspace><mi>𝛜</mi><mi>𝛝</mi><mi>𝛟</mi><mo>𝜘</mo><mo>𝜚</mo><mo>ϖ</mo><mi>𝟊</mi><mo>ϝ</mo><mspace width="0.222em"></mspace><mi>∂</mi><mi>∇</mi></mstyle><annotation encoding="application/x-tex">\mathbf{\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega \ \alpha \beta \gamma \delta \varepsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \pi \rho \varsigma \sigma \tau \upsilon \varphi \chi \psi \omega \ \epsilon \vartheta \phi \varkappa \varrho \varpi Ϝ\digamma \ \partial\nabla }</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="bold"><mn>0123456789</mn></mstyle><annotation encoding="application/x-tex">\mathbf{0123456789}</annotation></semantics></math></p>
</dd>
<dt>mathit:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="italic"><mi>𝐴</mi><mi>𝐵</mi><mi>𝐶</mi><mi>𝐷</mi><mi>𝐸</mi><mi>𝐹</mi><mi>𝐺</mi><mi>𝐻</mi><mi>𝐼</mi><mi>𝐽</mi><mi>𝐾</mi><mi>𝐿</mi><mi>𝑀</mi><mi>𝑁</mi><mi>𝑂</mi><mi>𝑃</mi><mi>𝑄</mi><mi>𝑅</mi><mi>𝑆</mi><mi>𝑇</mi><mi>𝑈</mi><mi>𝑉</mi><mi>𝑊</mi><mi>𝑋</mi><mi>𝑌</mi><mi>𝑍</mi><mspace width="0.222em"></mspace><mi>𝑎</mi><mi>𝑏</mi><mi>𝑐</mi><mi>𝑑</mi><mi>𝑒</mi><mi>𝑓</mi><mi>𝑔</mi><mi>h</mi><mi>𝑖</mi><mi>𝑗</mi><mi>𝑘</mi><mi>𝑙</mi><mi>𝑚</mi><mi>𝑛</mi><mi>𝑜</mi><mi>𝑝</mi><mi>𝑞</mi><mi>𝑟</mi><mi>𝑠</mi><mi>𝑡</mi><mi>𝑢</mi><mi>𝑣</mi><mi>𝑤</mi><mi>𝑥</mi><mi>𝑦</mi><mi>𝑧</mi><mspace width="0.222em"></mspace><mo>ı</mo><mo>ȷ</mo></mstyle><annotation encoding="application/x-tex">\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz\ \imath \jmath}</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="italic"><mi>𝛤</mi><mi>𝛥</mi><mi>𝛩</mi><mi>𝛬</mi><mi>𝛯</mi><mi>𝛱</mi><mi>𝛴</mi><mi>𝛶</mi><mi>𝛷</mi><mi>𝛹</mi><mi>𝛺</mi><mspace width="0.222em"></mspace><mi>𝛼</mi><mi>𝛽</mi><mi>𝛾</mi><mi>𝛿</mi><mi>𝜀</mi><mi>𝜁</mi><mi>𝜂</mi><mi>𝜃</mi><mi>𝜄</mi><mi>𝜅</mi><mi>𝜆</mi><mi>𝜇</mi><mi>𝜈</mi><mi>𝜉</mi><mi>𝜋</mi><mi>𝜌</mi><mo>ς</mo><mi>𝜎</mi><mi>𝜏</mi><mi>𝜐</mi><mi>𝜑</mi><mi>𝜒</mi><mi>𝜓</mi><mi>𝜔</mi><mspace width="0.222em"></mspace><mi>𝜖</mi><mi>𝜗</mi><mi>𝜙</mi><mo>𝜘</mo><mo>𝜚</mo><mo>ϖ</mo><mspace width="0.222em"></mspace><mi>∂</mi><mi>∇</mi></mstyle><annotation encoding="application/x-tex">\mathit{\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega \ \alpha \beta \gamma \delta \varepsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \pi \rho \varsigma \sigma \tau \upsilon \varphi \chi \psi \omega \ \epsilon \vartheta \phi \varkappa \varrho \varpi \ \partial\nabla }</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="italic"><mn>0123456789</mn></mstyle><annotation encoding="application/x-tex">\mathit{0123456789}</annotation></semantics></math> <a class="brackets" href="#italic-digits" id="footnote-reference-4" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a></p>
</dd>
<dt>mathbfit:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="bold-italic"><mi>𝑨</mi><mi>𝑩</mi><mi>𝑪</mi><mi>𝑫</mi><mi>𝑬</mi><mi>𝑭</mi><mi>𝑮</mi><mi>𝑯</mi><mi>𝑰</mi><mi>𝑱</mi><mi>𝑲</mi><mi>𝑳</mi><mi>𝑴</mi><mi>𝑵</mi><mi>𝑶</mi><mi>𝑷</mi><mi>𝑸</mi><mi>𝑹</mi><mi>𝑺</mi><mi>𝑻</mi><mi>𝑼</mi><mi>𝑽</mi><mi>𝑾</mi><mi>𝑿</mi><mi>𝒀</mi><mi>𝒁</mi><mspace width="0.222em"></mspace><mi>𝒂</mi><mi>𝒃</mi><mi>𝒄</mi><mi>𝒅</mi><mi>𝒆</mi><mi>𝒇</mi><mi>𝒈</mi><mi>𝒉</mi><mi>𝒊</mi><mi>𝒋</mi><mi>𝒌</mi><mi>𝒍</mi><mi>𝒎</mi><mi>𝒏</mi><mi>𝒐</mi><mi>𝒑</mi><mi>𝒒</mi><mi>𝒓</mi><mi>𝒔</mi><mi>𝒕</mi><mi>𝒖</mi><mi>𝒗</mi><mi>𝒘</mi><mi>𝒙</mi><mi>𝒚</mi><mi>𝒛</mi></mstyle><annotation encoding="application/x-tex">\mathbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="bold-italic"><mi>𝜞</mi><mi>𝜟</mi><mi>𝜣</mi><mi>𝜦</mi><mi>𝜩</mi><mi>𝜫</mi><mi>𝜮</mi><mi>𝜰</mi><mi>𝜱</mi><mi>𝜳</mi><mi>𝜴</mi><mspace width="0.222em"></mspace><mi>𝜶</mi><mi>𝜷</mi><mi>𝜸</mi><mi>𝜹</mi><mi>𝜺</mi><mi>𝜻</mi><mi>𝜼</mi><mi>𝜽</mi><mi>𝜾</mi><mi>𝜿</mi><mi>𝝀</mi><mi>𝝁</mi><mi>𝝂</mi><mi>𝝃</mi><mi>𝝅</mi><mi>𝝆</mi><mo>ς</mo><mi>𝝈</mi><mi>𝝉</mi><mi>𝝊</mi><mi>𝝋</mi><mi>𝝌</mi><mi>𝝍</mi><mi>𝝎</mi><mspace width="0.222em"></mspace><mi>𝝐</mi><mi>𝝑</mi><mi>𝝓</mi><mo>𝜘</mo><mo>𝜚</mo><mo>ϖ</mo><mspace width="0.222em"></mspace><mi>∂</mi><mi>∇</mi></mstyle><annotation encoding="application/x-tex">\mathbfit{\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega \ \alpha \beta \gamma \delta \varepsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \pi \rho \varsigma \sigma \tau \upsilon \varphi \chi \psi \omega \ \epsilon \vartheta \phi \varkappa \varrho \varpi \ \partial\nabla }</annotation></semantics></math></p>
</dd>
<dt>mathcal:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="script"><mi>𝒜</mi><mi>ℬ</mi><mi>𝒞</mi><mi>𝒟</mi><mi>ℰ</mi><mi>ℱ</mi><mi>𝒢</mi><mi>ℋ</mi><mi>ℐ</mi><mi>𝒥</mi><mi>𝒦</mi><mi>ℒ</mi><mi>ℳ</mi><mi>𝒩</mi><mi>𝒪</mi><mi>𝒫</mi><mi>𝒬</mi><mi>ℛ</mi><mi>𝒮</mi><mi>𝒯</mi><mi>𝒰</mi><mi>𝒱</mi><mi>𝒲</mi><mi>𝒳</mi><mi>𝒴</mi><mi>𝒵</mi><mspace width="0.222em"></mspace><mi>𝒶</mi><mi>𝒷</mi><mi>𝒸</mi><mi>𝒹</mi><mi>ℯ</mi><mi>𝒻</mi><mi>ℊ</mi><mi>𝒽</mi><mi>𝒾</mi><mi>𝒿</mi><mi>𝓀</mi><mi>𝓁</mi><mi>𝓂</mi><mi>𝓃</mi><mi>ℴ</mi><mi>𝓅</mi><mi>𝓆</mi><mi>𝓇</mi><mi>𝓈</mi><mi>𝓉</mi><mi>𝓊</mi><mi>𝓋</mi><mi>𝓌</mi><mi>𝓍</mi><mi>𝓎</mi><mi>𝓏</mi></mstyle><annotation encoding="application/x-tex">\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math></p>
</dd>
<dt>mathscr:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="script"><mi>𝒜</mi><mi>ℬ</mi><mi>𝒞</mi><mi>𝒟</mi><mi>ℰ</mi><mi>ℱ</mi><mi>𝒢</mi><mi>ℋ</mi><mi>ℐ</mi><mi>𝒥</mi><mi>𝒦</mi><mi>ℒ</mi><mi>ℳ</mi><mi>𝒩</mi><mi>𝒪</mi><mi>𝒫</mi><mi>𝒬</mi><mi>ℛ</mi><mi>𝒮</mi><mi>𝒯</mi><mi>𝒰</mi><mi>𝒱</mi><mi>𝒲</mi><mi>𝒳</mi><mi>𝒴</mi><mi>𝒵</mi><mspace width="0.222em"></mspace><mi>𝒶</mi><mi>𝒷</mi><mi>𝒸</mi><mi>𝒹</mi><mi>ℯ</mi><mi>𝒻</mi><mi>ℊ</mi><mi>𝒽</mi><mi>𝒾</mi><mi>𝒿</mi><mi>𝓀</mi><mi>𝓁</mi><mi>𝓂</mi><mi>𝓃</mi><mi>ℴ</mi><mi>𝓅</mi><mi>𝓆</mi><mi>𝓇</mi><mi>𝓈</mi><mi>𝓉</mi><mi>𝓊</mi><mi>𝓋</mi><mi>𝓌</mi><mi>𝓍</mi><mi>𝓎</mi><mi>𝓏</mi></mstyle><annotation encoding="application/x-tex">\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math></p>
</dd>
<dt>mathbb:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="double-struck"><mi>𝔸</mi><mi>𝔹</mi><mi>ℂ</mi><mi>𝔻</mi><mi>𝔼</mi><mi>𝔽</mi><mi>𝔾</mi><mi>ℍ</mi><mi>𝕀</mi><mi>𝕁</mi><mi>𝕂</mi><mi>𝕃</mi><mi>𝕄</mi><mi>ℕ</mi><mi>𝕆</mi><mi>ℙ</mi><mi>ℚ</mi><mi>ℝ</mi><mi>𝕊</mi><mi>𝕋</mi><mi>𝕌</mi><mi>𝕍</mi><mi>𝕎</mi><mi>𝕏</mi><mi>𝕐</mi><mi>ℤ</mi><mspace width="0.222em"></mspace><mi>𝕒</mi><mi>𝕓</mi><mi>𝕔</mi><mi>𝕕</mi><mi>𝕖</mi><mi>𝕗</mi><mi>𝕘</mi><mi>𝕙</mi><mi>𝕚</mi><mi>𝕛</mi><mi>𝕜</mi><mi>𝕝</mi><mi>𝕞</mi><mi>𝕟</mi><mi>𝕠</mi><mi>𝕡</mi><mi>𝕢</mi><mi>𝕣</mi><mi>𝕤</mi><mi>𝕥</mi><mi>𝕦</mi><mi>𝕧</mi><mi>𝕨</mi><mi>𝕩</mi><mi>𝕪</mi><mi>𝕫</mi></mstyle><annotation encoding="application/x-tex">\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="double-struck"><mi>ℾ</mi><mi>ℿ</mi><mi>Σ</mi><mspace width="0.222em"></mspace><mi>ℽ</mi><mi>ℼ</mi></mstyle><annotation encoding="application/x-tex">\mathbb{\Gamma \Pi \Sigma \ \gamma \pi }</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="double-struck"><mn>0123456789</mn></mstyle><annotation encoding="application/x-tex">\mathbb{0123456789}</annotation></semantics></math></p>
</dd>
<dt>mathfrak:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="fraktur"><mi>𝔄</mi><mi>𝔅</mi><mi>ℭ</mi><mi>𝔇</mi><mi>𝔈</mi><mi>𝔉</mi><mi>𝔊</mi><mi>ℌ</mi><mi>ℑ</mi><mi>𝔍</mi><mi>𝔎</mi><mi>𝔏</mi><mi>𝔐</mi><mi>𝔑</mi><mi>𝔒</mi><mi>𝔓</mi><mi>𝔔</mi><mi>ℜ</mi><mi>𝔖</mi><mi>𝔗</mi><mi>𝔘</mi><mi>𝔙</mi><mi>𝔚</mi><mi>𝔛</mi><mi>𝔜</mi><mi>ℨ</mi><mspace width="0.222em"></mspace><mi>𝔞</mi><mi>𝔟</mi><mi>𝔠</mi><mi>𝔡</mi><mi>𝔢</mi><mi>𝔣</mi><mi>𝔤</mi><mi>𝔥</mi><mi>𝔦</mi><mi>𝔧</mi><mi>𝔨</mi><mi>𝔩</mi><mi>𝔪</mi><mi>𝔫</mi><mi>𝔬</mi><mi>𝔭</mi><mi>𝔮</mi><mi>𝔯</mi><mi>𝔰</mi><mi>𝔱</mi><mi>𝔲</mi><mi>𝔳</mi><mi>𝔴</mi><mi>𝔵</mi><mi>𝔶</mi><mi>𝔷</mi></mstyle><annotation encoding="application/x-tex">\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math></p>
</dd>
<dt>mathsf:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="sans-serif"><mi>𝖠</mi><mi>𝖡</mi><mi>𝖢</mi><mi>𝖣</mi><mi>𝖤</mi><mi>𝖥</mi><mi>𝖦</mi><mi>𝖧</mi><mi>𝖨</mi><mi>𝖩</mi><mi>𝖪</mi><mi>𝖫</mi><mi>𝖬</mi><mi>𝖭</mi><mi>𝖮</mi><mi>𝖯</mi><mi>𝖰</mi><mi>𝖱</mi><mi>𝖲</mi><mi>𝖳</mi><mi>𝖴</mi><mi>𝖵</mi><mi>𝖶</mi><mi>𝖷</mi><mi>𝖸</mi><mi>𝖹</mi><mspace width="0.222em"></mspace><mi>𝖺</mi><mi>𝖻</mi><mi>𝖼</mi><mi>𝖽</mi><mi>𝖾</mi><mi>𝖿</mi><mi>𝗀</mi><mi>𝗁</mi><mi>𝗂</mi><mi>𝗃</mi><mi>𝗄</mi><mi>𝗅</mi><mi>𝗆</mi><mi>𝗇</mi><mi>𝗈</mi><mi>𝗉</mi><mi>𝗊</mi><mi>𝗋</mi><mi>𝗌</mi><mi>𝗍</mi><mi>𝗎</mi><mi>𝗏</mi><mi>𝗐</mi><mi>𝗑</mi><mi>𝗒</mi><mi>𝗓</mi></mstyle><annotation encoding="application/x-tex">\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="sans-serif"><mn>0123456789</mn></mstyle><annotation encoding="application/x-tex">\mathsf{0123456789}</annotation></semantics></math></p>
</dd>
<dt>mathsfit:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="sans-serif-italic"><mi>𝘈</mi><mi>𝘉</mi><mi>𝘊</mi><mi>𝘋</mi><mi>𝘌</mi><mi>𝘍</mi><mi>𝘎</mi><mi>𝘏</mi><mi>𝘐</mi><mi>𝘑</mi><mi>𝘒</mi><mi>𝘓</mi><mi>𝘔</mi><mi>𝘕</mi><mi>𝘖</mi><mi>𝘗</mi><mi>𝘘</mi><mi>𝘙</mi><mi>𝘚</mi><mi>𝘛</mi><mi>𝘜</mi><mi>𝘝</mi><mi>𝘞</mi><mi>𝘟</mi><mi>𝘠</mi><mi>𝘡</mi><mspace width="0.222em"></mspace><mi>𝘢</mi><mi>𝘣</mi><mi>𝘤</mi><mi>𝘥</mi><mi>𝘦</mi><mi>𝘧</mi><mi>𝘨</mi><mi>𝘩</mi><mi>𝘪</mi><mi>𝘫</mi><mi>𝘬</mi><mi>𝘭</mi><mi>𝘮</mi><mi>𝘯</mi><mi>𝘰</mi><mi>𝘱</mi><mi>𝘲</mi><mi>𝘳</mi><mi>𝘴</mi><mi>𝘵</mi><mi>𝘶</mi><mi>𝘷</mi><mi>𝘸</mi><mi>𝘹</mi><mi>𝘺</mi><mi>𝘻</mi></mstyle><annotation encoding="application/x-tex">\mathsfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math></p>
</dd>
<dt>mathsfbfit:</dt>
<dd><p><span class="math problematic m">\mathsfbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span>
<span class="math problematic m">\mathsfbfit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 416)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\mathsfbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}', rendering as TeX:</p>
<pre class="literal-block">  \mathsfbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\
             ^</pre>
<p class="pre-wrap">  unexpected &quot;{&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 416)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\mathsfbfit{\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega \ \alpha \beta \gamma \delta \varepsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \pi \rho \varsigma \sigma \tau \upsilon \varphi \chi \psi \omega \ \epsilon \vartheta \phi \varkappa \varrho \varpi \ \partial\nabla }', rendering as TeX:</p>
<pre class="literal-block">  \mathsfbfit{\Gamma \Delta \Theta \Lambda
             ^</pre>
<p class="pre-wrap">  unexpected &quot;{&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</dd>
<dt>mathtt:</dt>
<dd><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="monospace"><mi>𝙰</mi><mi>𝙱</mi><mi>𝙲</mi><mi>𝙳</mi><mi>𝙴</mi><mi>𝙵</mi><mi>𝙶</mi><mi>𝙷</mi><mi>𝙸</mi><mi>𝙹</mi><mi>𝙺</mi><mi>𝙻</mi><mi>𝙼</mi><mi>𝙽</mi><mi>𝙾</mi><mi>𝙿</mi><mi>𝚀</mi><mi>𝚁</mi><mi>𝚂</mi><mi>𝚃</mi><mi>𝚄</mi><mi>𝚅</mi><mi>𝚆</mi><mi>𝚇</mi><mi>𝚈</mi><mi>𝚉</mi><mspace width="0.222em"></mspace><mi>𝚊</mi><mi>𝚋</mi><mi>𝚌</mi><mi>𝚍</mi><mi>𝚎</mi><mi>𝚏</mi><mi>𝚐</mi><mi>𝚑</mi><mi>𝚒</mi><mi>𝚓</mi><mi>𝚔</mi><mi>𝚕</mi><mi>𝚖</mi><mi>𝚗</mi><mi>𝚘</mi><mi>𝚙</mi><mi>𝚚</mi><mi>𝚛</mi><mi>𝚜</mi><mi>𝚝</mi><mi>𝚞</mi><mi>𝚟</mi><mi>𝚠</mi><mi>𝚡</mi><mi>𝚢</mi><mi>𝚣</mi></mstyle><annotation encoding="application/x-tex">\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</annotation></semantics></math>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="monospace"><mn>0123456789</mn></mstyle><annotation encoding="application/x-tex">\mathtt{0123456789}</annotation></semantics></math></p>
</dd>
</dl>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="italic-digits" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#footnote-reference-3">1</a>,<a role="doc-backlink" href="#footnote-reference-4">2</a>)</span>
<p>Italic digits are not defined in Unicode
but work in LaTeX.</p>
</aside>
</aside>
<p>In contrast to the <em>math alphabet</em> selectors, <span class="docutils literal">\boldsymbol</span> only
changes the <em>font weight</em>. It can be used to get a bold version of
any mathematical symbol:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub><mi>x</mi><mo>±</mo><mo>cos</mo><mo stretchy="false" form="prefix">(</mo><mi>α</mi><mo stretchy="false" form="postfix">)</mo><mo>≈</mo><mn>3</mn><mi>Γ</mi><mspace width="1.0em"></mspace><mo>∀</mo><mi>x</mi><mo>∈</mo><mstyle mathvariant="double-struck"><mi>ℝ</mi></mstyle></mrow><annotation encoding="application/x-tex">V_i x \pm \cos(\alpha) \approx 3\Gamma \quad \forall x\in\mathbb{R}</annotation></semantics></math>
</div>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle mathvariant="bold"><msub><mi>𝐕</mi><mi>𝐢</mi></msub><mi>𝐱</mi><mo>±</mo><mo>cos</mo><mo stretchy="false" form="prefix">(</mo><mi>𝛂</mi><mo stretchy="false" form="postfix">)</mo><mo>≈</mo><mn>3</mn><mi>𝚪</mi><mspace width="1.0em"></mspace><mo>∀</mo><mi>𝐱</mi><mo>∈</mo><mstyle mathvariant="double-struck"><mi>ℝ</mi></mstyle></mstyle><annotation encoding="application/x-tex">\boldsymbol{V_i x \pm \cos(\alpha) \approx 3\Gamma \quad \forall x\in\mathbb{R}}</annotation></semantics></math>
</div>
<p>It is usually ill-advised to apply <span class="docutils literal">\boldsymbol</span> to more than one symbol
at a time.</p>
</section>
<section id="miscellaneous-symbols">
<h3><a class="toc-backref" href="#toc-entry-13" role="doc-backlink"><span class="sectnum">2.9 </span>Miscellaneous symbols</a></h3>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>#</mi><annotation encoding="application/x-tex">\#</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\#</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>♣</mi><annotation encoding="application/x-tex">\clubsuit</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\clubsuit</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>¬</mo><annotation encoding="application/x-tex">\neg</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\neg</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>&amp;</mi><annotation encoding="application/x-tex">\&amp;</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\&amp;</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>♢</mi><annotation encoding="application/x-tex">\diamondsuit</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\diamondsuit</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∄</mi><annotation encoding="application/x-tex">\nexists</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nexists</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∠</mi><annotation encoding="application/x-tex">\angle</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\angle</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∅</mi><annotation encoding="application/x-tex">\emptyset</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\emptyset</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>′</mi><annotation encoding="application/x-tex">\prime</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\prime</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>‵</mi><annotation encoding="application/x-tex">\backprime</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\backprime</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∃</mo><annotation encoding="application/x-tex">\exists</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\exists</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>♯</mi><annotation encoding="application/x-tex">\sharp</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sharp</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>★</mi><annotation encoding="application/x-tex">\bigstar</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bigstar</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>♭</mi><annotation encoding="application/x-tex">\flat</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\flat</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>♠</mi><annotation encoding="application/x-tex">\spadesuit</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\spadesuit</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⬧</mi><annotation encoding="application/x-tex">\blacklozenge</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\blacklozenge</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∀</mo><annotation encoding="application/x-tex">\forall</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\forall</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∢</mi><annotation encoding="application/x-tex">\sphericalangle</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sphericalangle</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>◼</mi><annotation encoding="application/x-tex">\blacksquare</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\blacksquare</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>♡</mi><annotation encoding="application/x-tex">\heartsuit</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\heartsuit</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>▫</mi><annotation encoding="application/x-tex">\square</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\square</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>▴</mo><annotation encoding="application/x-tex">\blacktriangle</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\blacktriangle</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∞</mi><annotation encoding="application/x-tex">\infty</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\infty</span></p></td>
<td><p><span class="math problematic m">\surd</span></p></td>
<td><p><span class="docutils literal">\surd</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>▾</mo><annotation encoding="application/x-tex">\blacktriangledown</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\blacktriangledown</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>◊</mo><annotation encoding="application/x-tex">\lozenge</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lozenge</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⊤</mi><annotation encoding="application/x-tex">\top</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\top</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⊥</mi><annotation encoding="application/x-tex">\bot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∡</mi><annotation encoding="application/x-tex">\measuredangle</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\measuredangle</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>△</mi><annotation encoding="application/x-tex">\triangle</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\triangle</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\diagdown</span></p></td>
<td><p><span class="docutils literal">\diagdown</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∇</mi><annotation encoding="application/x-tex">\nabla</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nabla</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>▿</mo><annotation encoding="application/x-tex">\triangledown</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\triangledown</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\diagup</span></p></td>
<td><p><span class="docutils literal">\diagup</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>♮</mi><annotation encoding="application/x-tex">\natural</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\natural</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⌀</mi><annotation encoding="application/x-tex">\varnothing</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\varnothing</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 458)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\surd', rendering as TeX:</p>
<pre class="literal-block">  \surd
       ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting letter, &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot;, whitespace, &quot;[&quot;, &quot;\\not&quot;, &quot;!&quot;, &quot;'&quot;, &quot;''&quot;, &quot;'''&quot;, &quot;''''&quot;, &quot;*&quot;, &quot;+&quot;, &quot;,&quot;, &quot;-&quot;, &quot;.&quot;, &quot;/&quot;, &quot;:&quot;, &quot;:=&quot;, &quot;;&quot;, &quot;&lt;&quot;, &quot;=&quot;, &quot;&gt;&quot;, &quot;?&quot;, &quot;&#64;&quot;, &quot;~&quot;, &quot;\\&quot; or &quot;{&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 461)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\diagdown', rendering as TeX:</p>
<pre class="literal-block">  \diagdown
           ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 462)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\diagup', rendering as TeX:</p>
<pre class="literal-block">  \diagup
         ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</section>
<section id="punctuation">
<h3><a class="toc-backref" href="#toc-entry-14" role="doc-backlink"><span class="sectnum">2.10 </span>Punctuation</a></h3>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>.</mi><annotation encoding="application/x-tex">.</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">.</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>!</mi><annotation encoding="application/x-tex">!</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">!</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⋮</mi><annotation encoding="application/x-tex">\vdots</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vdots</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>/</mi><annotation encoding="application/x-tex">/</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">/</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>?</mi><annotation encoding="application/x-tex">?</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">?</span></p></td>
<td><p><span class="math problematic m">\dotsb</span></p></td>
<td><p><span class="docutils literal">\dotsb</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo stretchy="false" form="prefix">|</mo><annotation encoding="application/x-tex">|</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">|</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>:</mo><annotation encoding="application/x-tex">\colon</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\colon</span> <a class="brackets" href="#footnote-1" id="footnote-reference-5" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a></p></td>
<td><p><span class="math problematic m">\dotsc</span></p></td>
<td><p><span class="docutils literal">\dotsc</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>′</mi><annotation encoding="application/x-tex">&#39;</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">'</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⋯</mi><annotation encoding="application/x-tex">\cdots</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\cdots</span></p></td>
<td><p><span class="math problematic m">\dotsi</span></p></td>
<td><p><span class="docutils literal">\dotsi</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>;</mo><annotation encoding="application/x-tex">;</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">;</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⋱</mi><annotation encoding="application/x-tex">\ddots</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ddots</span></p></td>
<td><p><span class="math problematic m">\dotsm</span></p></td>
<td><p><span class="docutils literal">\dotsm</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>:</mo><annotation encoding="application/x-tex">:</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">:</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>…</mi><annotation encoding="application/x-tex">\ldots</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ldots</span></p></td>
<td><p><span class="math problematic m">\dotso</span></p></td>
<td><p><span class="docutils literal">\dotso</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 472)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\dotsb', rendering as TeX:</p>
<pre class="literal-block">  \dotsb
        ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 473)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\dotsc', rendering as TeX:</p>
<pre class="literal-block">  \dotsc
        ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 474)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\dotsi', rendering as TeX:</p>
<pre class="literal-block">  \dotsi
        ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 475)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\dotsm', rendering as TeX:</p>
<pre class="literal-block">  \dotsm
        ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 476)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\dotso', rendering as TeX:</p>
<pre class="literal-block">  \dotso
        ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-1" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-5">3</a><span class="fn-bracket">]</span></span>
<p>Punctuation (not ratio):
Compare spacing in <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo>:</mo><mi>b</mi><mo>→</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">a\colon b\to c</annotation></semantics></math> to <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo>:</mo><mi>b</mi><mo>=</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">a:b = c</annotation></semantics></math>.</p>
</aside>
</aside>
</section>
<section id="relation-symbols">
<h3><a class="toc-backref" href="#toc-entry-15" role="doc-backlink"><span class="sectnum">2.11 </span>Relation symbols</a></h3>
<section id="arrows">
<h4><a class="toc-backref" href="#toc-entry-16" role="doc-backlink"><span class="sectnum">2.11.1 </span>Arrows</a></h4>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>↺</mi><annotation encoding="application/x-tex">\circlearrowleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\circlearrowleft</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>↻</mi><annotation encoding="application/x-tex">\circlearrowright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\circlearrowright</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↶</mo><annotation encoding="application/x-tex">\curvearrowleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\curvearrowleft</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↷</mo><annotation encoding="application/x-tex">\curvearrowright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\curvearrowright</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↩</mo><annotation encoding="application/x-tex">\hookleftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\hookleftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↪</mo><annotation encoding="application/x-tex">\hookrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\hookrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>←</mo><annotation encoding="application/x-tex">\leftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>→</mo><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇐</mo><annotation encoding="application/x-tex">\Leftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Leftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇒</mo><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Rightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↢</mo><annotation encoding="application/x-tex">\leftarrowtail</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftarrowtail</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↣</mo><annotation encoding="application/x-tex">\rightarrowtail</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightarrowtail</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↽</mo><annotation encoding="application/x-tex">\leftharpoondown</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftharpoondown</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇁</mo><annotation encoding="application/x-tex">\rightharpoondown</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightharpoondown</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↼</mo><annotation encoding="application/x-tex">\leftharpoonup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftharpoonup</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇀</mo><annotation encoding="application/x-tex">\rightharpoonup</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightharpoonup</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇇</mo><annotation encoding="application/x-tex">\leftleftarrows</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftleftarrows</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇉</mo><annotation encoding="application/x-tex">\rightrightarrows</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightrightarrows</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↔</mo><annotation encoding="application/x-tex">\leftrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftrightarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇔</mo><annotation encoding="application/x-tex">\Leftrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Leftrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇆</mo><annotation encoding="application/x-tex">\leftrightarrows</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftrightarrows</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇄</mo><annotation encoding="application/x-tex">\rightleftarrows</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightleftarrows</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇋</mo><annotation encoding="application/x-tex">\leftrightharpoons</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftrightharpoons</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇌</mo><annotation encoding="application/x-tex">\rightleftharpoons</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightleftharpoons</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↭</mo><annotation encoding="application/x-tex">\leftrightsquigarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leftrightsquigarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇝</mo><annotation encoding="application/x-tex">\rightsquigarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\rightsquigarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇚</mo><annotation encoding="application/x-tex">\Lleftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Lleftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇛</mo><annotation encoding="application/x-tex">\Rrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Rrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>←</mo><annotation encoding="application/x-tex">\longleftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\longleftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>→</mo><annotation encoding="application/x-tex">\longrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\longrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇐</mo><annotation encoding="application/x-tex">\Longleftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Longleftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇒</mo><annotation encoding="application/x-tex">\Longrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Longrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↔</mo><annotation encoding="application/x-tex">\longleftrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\longleftrightarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇔</mo><annotation encoding="application/x-tex">\Longleftrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Longleftrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↫</mo><annotation encoding="application/x-tex">\looparrowleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\looparrowleft</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↬</mo><annotation encoding="application/x-tex">\looparrowright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\looparrowright</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↰</mo><annotation encoding="application/x-tex">\Lsh</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Lsh</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↱</mo><annotation encoding="application/x-tex">\Rsh</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Rsh</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↦</mo><annotation encoding="application/x-tex">\mapsto</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\mapsto</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↦</mo><annotation encoding="application/x-tex">\longmapsto</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\longmapsto</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊸</mo><annotation encoding="application/x-tex">\multimap</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\multimap</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↚</mo><annotation encoding="application/x-tex">\nleftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nleftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↛</mo><annotation encoding="application/x-tex">\nrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇍</mo><annotation encoding="application/x-tex">\nLeftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nLeftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇏</mo><annotation encoding="application/x-tex">\nRightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nRightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↮</mo><annotation encoding="application/x-tex">\nleftrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nleftrightarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇎</mo><annotation encoding="application/x-tex">\nLeftrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nLeftrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↖</mo><annotation encoding="application/x-tex">\nwarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nwarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↗</mo><annotation encoding="application/x-tex">\nearrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nearrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↙</mo><annotation encoding="application/x-tex">\swarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\swarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↘</mo><annotation encoding="application/x-tex">\searrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\searrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↞</mo><annotation encoding="application/x-tex">\twoheadleftarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\twoheadleftarrow</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↠</mo><annotation encoding="application/x-tex">\twoheadrightarrow</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\twoheadrightarrow</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↿</mo><annotation encoding="application/x-tex">\upharpoonleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\upharpoonleft</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↾</mo><annotation encoding="application/x-tex">\upharpoonright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\upharpoonright</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇃</mo><annotation encoding="application/x-tex">\downharpoonleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\downharpoonleft</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇂</mo><annotation encoding="application/x-tex">\downharpoonright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\downharpoonright</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇈</mo><annotation encoding="application/x-tex">\upuparrows</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\upuparrows</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇊</mo><annotation encoding="application/x-tex">\downdownarrows</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\downdownarrows</span></p></td>
</tr>
</tbody>
</table>
<p>Synonyms: <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>←</mo><annotation encoding="application/x-tex">\gets</annotation></semantics></math> <span class="docutils literal">\gets</span>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>→</mo><annotation encoding="application/x-tex">\to</annotation></semantics></math> <span class="docutils literal">\to</span>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↾</mo><annotation encoding="application/x-tex">\restriction</annotation></semantics></math> <span class="docutils literal">\restriction</span>.</p>
</section>
<section id="comparison">
<h4><a class="toc-backref" href="#toc-entry-17" role="doc-backlink"><span class="sectnum">2.11.2 </span>Comparison</a></h4>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>&lt;</mo><annotation encoding="application/x-tex">&lt;</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">&lt;</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≥</mo><annotation encoding="application/x-tex">\geq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\geq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≪</mo><annotation encoding="application/x-tex">\ll</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ll</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≺</mo><annotation encoding="application/x-tex">\prec</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\prec</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>=</mo><annotation encoding="application/x-tex">=</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">=</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≧</mo><annotation encoding="application/x-tex">\geqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\geqq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋘</mo><annotation encoding="application/x-tex">\lll</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lll</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪷</mo><annotation encoding="application/x-tex">\precapprox</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\precapprox</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>&gt;</mo><annotation encoding="application/x-tex">&gt;</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">&gt;</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≥</mo><annotation encoding="application/x-tex">\geqslant</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\geqslant</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪉</mo><annotation encoding="application/x-tex">\lnapprox</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lnapprox</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≼</mo><annotation encoding="application/x-tex">\preccurlyeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\preccurlyeq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≈</mo><annotation encoding="application/x-tex">\approx</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\approx</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≫</mo><annotation encoding="application/x-tex">\gg</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gg</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪇</mo><annotation encoding="application/x-tex">\lneq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lneq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≼</mo><annotation encoding="application/x-tex">\preceq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\preceq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≊</mo><annotation encoding="application/x-tex">\approxeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\approxeq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋙</mo><annotation encoding="application/x-tex">\ggg</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ggg</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≨</mo><annotation encoding="application/x-tex">\lneqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lneqq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪹</mo><annotation encoding="application/x-tex">\precnapprox</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\precnapprox</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≍</mo><annotation encoding="application/x-tex">\asymp</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\asymp</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪊</mo><annotation encoding="application/x-tex">\gnapprox</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gnapprox</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋦</mo><annotation encoding="application/x-tex">\lnsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lnsim</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪵</mo><annotation encoding="application/x-tex">\precneqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\precneqq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∽</mo><annotation encoding="application/x-tex">\backsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\backsim</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪈</mo><annotation encoding="application/x-tex">\gneq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gneq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≇</mo><annotation encoding="application/x-tex">\ncong</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ncong</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋨</mo><annotation encoding="application/x-tex">\precnsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\precnsim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋍</mo><annotation encoding="application/x-tex">\backsimeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\backsimeq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≩</mo><annotation encoding="application/x-tex">\gneqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gneqq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≠</mo><annotation encoding="application/x-tex">\neq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\neq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≾</mo><annotation encoding="application/x-tex">\precsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\precsim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≏</mo><annotation encoding="application/x-tex">\bumpeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bumpeq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋧</mo><annotation encoding="application/x-tex">\gnsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gnsim</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≱</mo><annotation encoding="application/x-tex">\ngeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ngeq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≓</mo><annotation encoding="application/x-tex">\risingdotseq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\risingdotseq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≎</mo><annotation encoding="application/x-tex">\Bumpeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Bumpeq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪆</mo><annotation encoding="application/x-tex">\gtrapprox</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gtrapprox</span></p></td>
<td><p><span class="math problematic m">\ngeqq</span></p></td>
<td><p><span class="docutils literal">\ngeqq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∼</mo><annotation encoding="application/x-tex">\sim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≗</mo><annotation encoding="application/x-tex">\circeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\circeq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋛</mo><annotation encoding="application/x-tex">\gtreqless</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gtreqless</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≱</mo><annotation encoding="application/x-tex">\ngeqslant</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ngeqslant</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≃</mo><annotation encoding="application/x-tex">\simeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\simeq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≅</mo><annotation encoding="application/x-tex">\cong</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\cong</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪌</mo><annotation encoding="application/x-tex">\gtreqqless</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gtreqqless</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≯</mo><annotation encoding="application/x-tex">\ngtr</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ngtr</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≻</mo><annotation encoding="application/x-tex">\succ</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\succ</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋞</mo><annotation encoding="application/x-tex">\curlyeqprec</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\curlyeqprec</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≷</mo><annotation encoding="application/x-tex">\gtrless</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gtrless</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≰</mo><annotation encoding="application/x-tex">\nleq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nleq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪸</mo><annotation encoding="application/x-tex">\succapprox</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\succapprox</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋟</mo><annotation encoding="application/x-tex">\curlyeqsucc</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\curlyeqsucc</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≳</mo><annotation encoding="application/x-tex">\gtrsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\gtrsim</span></p></td>
<td><p><span class="math problematic m">\nleqq</span></p></td>
<td><p><span class="docutils literal">\nleqq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≽</mo><annotation encoding="application/x-tex">\succcurlyeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\succcurlyeq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≐</mo><annotation encoding="application/x-tex">\doteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\doteq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≤</mo><annotation encoding="application/x-tex">\leq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≰</mo><annotation encoding="application/x-tex">\nleqslant</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nleqslant</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≽</mo><annotation encoding="application/x-tex">\succeq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\succeq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≑</mo><annotation encoding="application/x-tex">\doteqdot</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\doteqdot</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≦</mo><annotation encoding="application/x-tex">\leqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leqq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≮</mo><annotation encoding="application/x-tex">\nless</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nless</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪺</mo><annotation encoding="application/x-tex">\succnapprox</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\succnapprox</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≖</mo><annotation encoding="application/x-tex">\eqcirc</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\eqcirc</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≤</mo><annotation encoding="application/x-tex">\leqslant</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\leqslant</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊀</mo><annotation encoding="application/x-tex">\nprec</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nprec</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪶</mo><annotation encoding="application/x-tex">\succneqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\succneqq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≂</mo><annotation encoding="application/x-tex">\eqsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\eqsim</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪅</mo><annotation encoding="application/x-tex">\lessapprox</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lessapprox</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋠</mo><annotation encoding="application/x-tex">\npreceq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\npreceq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋩</mo><annotation encoding="application/x-tex">\succnsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\succnsim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪖</mo><annotation encoding="application/x-tex">\eqslantgtr</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\eqslantgtr</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋚</mo><annotation encoding="application/x-tex">\lesseqgtr</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lesseqgtr</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≁</mo><annotation encoding="application/x-tex">\nsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nsim</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≿</mo><annotation encoding="application/x-tex">\succsim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\succsim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪕</mo><annotation encoding="application/x-tex">\eqslantless</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\eqslantless</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⪋</mo><annotation encoding="application/x-tex">\lesseqqgtr</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lesseqqgtr</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊁</mo><annotation encoding="application/x-tex">\nsucc</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nsucc</span></p></td>
<td><p><span class="math problematic m">\thickapprox</span></p></td>
<td><p><span class="docutils literal">\thickapprox</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≡</mo><annotation encoding="application/x-tex">\equiv</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\equiv</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≶</mo><annotation encoding="application/x-tex">\lessgtr</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lessgtr</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋡</mo><annotation encoding="application/x-tex">\nsucceq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nsucceq</span></p></td>
<td><p><span class="math problematic m">\thicksim</span></p></td>
<td><p><span class="docutils literal">\thicksim</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≒</mo><annotation encoding="application/x-tex">\fallingdotseq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\fallingdotseq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≲</mo><annotation encoding="application/x-tex">\lesssim</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\lesssim</span></p></td>
<td></td>
<td></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≜</mo><annotation encoding="application/x-tex">\triangleq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\triangleq</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 540)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\ngeqq', rendering as TeX:</p>
<pre class="literal-block">  \ngeqq
        ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 544)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\nleqq', rendering as TeX:</p>
<pre class="literal-block">  \nleqq
        ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 550)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\thickapprox', rendering as TeX:</p>
<pre class="literal-block">  \thickapprox
              ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 551)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\thicksim', rendering as TeX:</p>
<pre class="literal-block">  \thicksim
           ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>The commands <span class="docutils literal">\lvertneqq</span> and <span class="docutils literal">\gvertneqq</span> are not supported
with MathML output, as there is no corresponding Unicode character.</p>
<p>Synonyms: <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≠</mo><annotation encoding="application/x-tex">\ne</annotation></semantics></math> <span class="docutils literal">\ne</span>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≤</mo><annotation encoding="application/x-tex">\le</annotation></semantics></math> <span class="docutils literal">\le</span>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≥</mo><annotation encoding="application/x-tex">\ge</annotation></semantics></math> <span class="docutils literal">\ge</span>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≑</mo><annotation encoding="application/x-tex">\Doteq</annotation></semantics></math> <span class="docutils literal">\Doteq</span>, <span class="math problematic m">\llless</span> <span class="docutils literal">\llless</span>, <span class="math problematic m">\gggtr</span> <span class="docutils literal">\gggtr</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 558)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\llless', rendering as TeX:</p>
<pre class="literal-block">  \llless
         ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 558)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\gggtr', rendering as TeX:</p>
<pre class="literal-block">  \gggtr
        ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>Symbols can be negated prepending <span class="docutils literal">\not</span>, e.g.
<span class="math problematic m">\not=</span> <span class="docutils literal">\not=</span>, <span class="math problematic m">\not\equiv</span> <span class="docutils literal">\not\equiv</span>,
<span class="math problematic m">\not\gtrless</span> <span class="docutils literal">\not\gtrless</span>, <span class="math problematic m">\not\lessgtr</span> <span class="docutils literal">\not\lessgtr</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 561)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\not=', rendering as TeX:</p>
<pre class="literal-block">  \not=
       ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 561)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\not\equiv', rendering as TeX:</p>
<pre class="literal-block">  \not\equiv
            ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 561)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\not\gtrless', rendering as TeX:</p>
<pre class="literal-block">  \not\gtrless
              ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 561)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\not\lessgtr', rendering as TeX:</p>
<pre class="literal-block">  \not\lessgtr
              ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</section>
<section id="miscellaneous-relations">
<h4><a class="toc-backref" href="#toc-entry-18" role="doc-backlink"><span class="sectnum">2.11.3 </span>Miscellaneous relations</a></h4>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>϶</mi><annotation encoding="application/x-tex">\backepsilon</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\backepsilon</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋬</mo><annotation encoding="application/x-tex">\ntrianglelefteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ntrianglelefteq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊆</mo><annotation encoding="application/x-tex">\subseteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\subseteq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∵</mi><annotation encoding="application/x-tex">\because</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\because</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋫</mo><annotation encoding="application/x-tex">\ntriangleright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ntriangleright</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⫅</mo><annotation encoding="application/x-tex">\subseteqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\subseteqq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≬</mo><annotation encoding="application/x-tex">\between</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\between</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋭</mo><annotation encoding="application/x-tex">\ntrianglerighteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ntrianglerighteq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊊</mo><annotation encoding="application/x-tex">\subsetneq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\subsetneq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>◂</mo><annotation encoding="application/x-tex">\blacktriangleleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\blacktriangleleft</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊬</mo><annotation encoding="application/x-tex">\nvdash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nvdash</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⫋</mo><annotation encoding="application/x-tex">\subsetneqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\subsetneqq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>▸</mo><annotation encoding="application/x-tex">\blacktriangleright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\blacktriangleright</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊮</mo><annotation encoding="application/x-tex">\nVdash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nVdash</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊃</mo><annotation encoding="application/x-tex">\supset</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\supset</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋈</mo><annotation encoding="application/x-tex">\bowtie</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\bowtie</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊭</mo><annotation encoding="application/x-tex">\nvDash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nvDash</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋑</mo><annotation encoding="application/x-tex">\Supset</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Supset</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊣</mo><annotation encoding="application/x-tex">\dashv</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\dashv</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊯</mo><annotation encoding="application/x-tex">\nVDash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nVDash</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊇</mo><annotation encoding="application/x-tex">\supseteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\supseteq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⌢</mo><annotation encoding="application/x-tex">\frown</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\frown</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∥</mo><annotation encoding="application/x-tex">\parallel</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\parallel</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⫆</mo><annotation encoding="application/x-tex">\supseteqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\supseteqq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∈</mo><annotation encoding="application/x-tex">\in</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\in</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊥</mo><annotation encoding="application/x-tex">\perp</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\perp</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊋</mo><annotation encoding="application/x-tex">\supsetneq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\supsetneq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∣</mo><annotation encoding="application/x-tex">\mid</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\mid</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋔</mo><annotation encoding="application/x-tex">\pitchfork</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\pitchfork</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⫌</mo><annotation encoding="application/x-tex">\supsetneqq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\supsetneqq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊨</mo><annotation encoding="application/x-tex">\models</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\models</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∝</mo><annotation encoding="application/x-tex">\propto</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\propto</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∴</mo><annotation encoding="application/x-tex">\therefore</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\therefore</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∋</mo><annotation encoding="application/x-tex">\ni</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ni</span></p></td>
<td><p><span class="math problematic m">\shortmid</span></p></td>
<td><p><span class="docutils literal">\shortmid</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊴</mo><annotation encoding="application/x-tex">\trianglelefteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\trianglelefteq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∤</mo><annotation encoding="application/x-tex">\nmid</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nmid</span></p></td>
<td><p><span class="math problematic m">\shortparallel</span></p></td>
<td><p><span class="docutils literal">\shortparallel</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊵</mo><annotation encoding="application/x-tex">\trianglerighteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\trianglerighteq</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∉</mo><annotation encoding="application/x-tex">\notin</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\notin</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⌢</mo><annotation encoding="application/x-tex">\smallfrown</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\smallfrown</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∝</mo><annotation encoding="application/x-tex">\varpropto</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\varpropto</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∦</mo><annotation encoding="application/x-tex">\nparallel</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nparallel</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⌣</mo><annotation encoding="application/x-tex">\smallsmile</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\smallsmile</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>▵</mo><annotation encoding="application/x-tex">\vartriangle</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vartriangle</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\nshortmid</span></p></td>
<td><p><span class="docutils literal">\nshortmid</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⌣</mo><annotation encoding="application/x-tex">\smile</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\smile</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊲</mo><annotation encoding="application/x-tex">\vartriangleleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vartriangleleft</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\nshortparallel</span></p></td>
<td><p><span class="docutils literal">\nshortparallel</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊏</mo><annotation encoding="application/x-tex">\sqsubset</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sqsubset</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊳</mo><annotation encoding="application/x-tex">\vartriangleright</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vartriangleright</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊈</mo><annotation encoding="application/x-tex">\nsubseteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nsubseteq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊑</mo><annotation encoding="application/x-tex">\sqsubseteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sqsubseteq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊢</mo><annotation encoding="application/x-tex">\vdash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vdash</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\nsubseteqq</span></p></td>
<td><p><span class="docutils literal">\nsubseteqq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊐</mo><annotation encoding="application/x-tex">\sqsupset</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sqsupset</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊩</mo><annotation encoding="application/x-tex">\Vdash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Vdash</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊉</mo><annotation encoding="application/x-tex">\nsupseteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\nsupseteq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊒</mo><annotation encoding="application/x-tex">\sqsupseteq</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\sqsupseteq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊨</mo><annotation encoding="application/x-tex">\vDash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\vDash</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\nsupseteqq</span></p></td>
<td><p><span class="docutils literal">\nsupseteqq</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊂</mo><annotation encoding="application/x-tex">\subset</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\subset</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊪</mo><annotation encoding="application/x-tex">\Vvdash</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Vvdash</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋪</mo><annotation encoding="application/x-tex">\ntriangleleft</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\ntriangleleft</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋐</mo><annotation encoding="application/x-tex">\Subset</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">\Subset</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 581)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\shortmid', rendering as TeX:</p>
<pre class="literal-block">  \shortmid
           ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 582)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\shortparallel', rendering as TeX:</p>
<pre class="literal-block">  \shortparallel
                ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 585)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\nshortmid', rendering as TeX:</p>
<pre class="literal-block">  \nshortmid
            ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 586)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\nshortparallel', rendering as TeX:</p>
<pre class="literal-block">  \nshortparallel
                 ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 588)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\nsubseteqq', rendering as TeX:</p>
<pre class="literal-block">  \nsubseteqq
             ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 590)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\nsupseteqq', rendering as TeX:</p>
<pre class="literal-block">  \nsupseteqq
             ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>Synonyms: <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∋</mo><annotation encoding="application/x-tex">\owns</annotation></semantics></math> <span class="docutils literal">\owns</span>.</p>
<p>Symbols can be negated prepending <span class="docutils literal">\not</span>, e.g.
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∉</mo><annotation encoding="application/x-tex">\not\in</annotation></semantics></math> <span class="docutils literal">\not\in</span>, <span class="math problematic m">\not\ni</span> <span class="docutils literal">\not\ni</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 596)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\not\ni', rendering as TeX:</p>
<pre class="literal-block">  \not\ni
         ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>The commands <span class="docutils literal">\varsubsetneq</span>, <span class="docutils literal">\varsubsetneqq</span>, <span class="docutils literal">\varsupsetneq</span>,
and <span class="docutils literal">\varsupsetneqq</span> are not supported with MathML output as there is no
corresponding Unicode character.</p>
</section>
</section>
<section id="variable-sized-operators">
<h3><a class="toc-backref" href="#toc-entry-19" role="doc-backlink"><span class="sectnum">2.12 </span>Variable-sized operators</a></h3>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∑</mo><annotation encoding="application/x-tex">\sum</annotation></semantics></math>      <span class="docutils literal">\sum</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∏</mo><annotation encoding="application/x-tex">\prod</annotation></semantics></math>     <span class="docutils literal">\prod</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋂</mo><annotation encoding="application/x-tex">\bigcap</annotation></semantics></math>   <span class="docutils literal">\bigcap</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⨀</mo><annotation encoding="application/x-tex">\bigodot</annotation></semantics></math>   <span class="docutils literal">\bigodot</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∫</mo><annotation encoding="application/x-tex">\int</annotation></semantics></math>      <span class="docutils literal">\int</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∐</mo><annotation encoding="application/x-tex">\coprod</annotation></semantics></math>   <span class="docutils literal">\coprod</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋃</mo><annotation encoding="application/x-tex">\bigcup</annotation></semantics></math>   <span class="docutils literal">\bigcup</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⨁</mo><annotation encoding="application/x-tex">\bigoplus</annotation></semantics></math>  <span class="docutils literal">\bigoplus</span></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∮</mo><annotation encoding="application/x-tex">\oint</annotation></semantics></math>     <span class="docutils literal">\oint</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋀</mo><annotation encoding="application/x-tex">\bigwedge</annotation></semantics></math> <span class="docutils literal">\bigwedge</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⨄</mo><annotation encoding="application/x-tex">\biguplus</annotation></semantics></math> <span class="docutils literal">\biguplus</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⨂</mo><annotation encoding="application/x-tex">\bigotimes</annotation></semantics></math> <span class="docutils literal">\bigotimes</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\smallint</span> <span class="docutils literal">\smallint</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋁</mo><annotation encoding="application/x-tex">\bigvee</annotation></semantics></math>   <span class="docutils literal">\bigvee</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⨆</mo><annotation encoding="application/x-tex">\bigsqcup</annotation></semantics></math> <span class="docutils literal">\bigsqcup</span></p></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 612)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\smallint', rendering as TeX:</p>
<pre class="literal-block">  \smallint
           ^</pre>
<p class="pre-wrap">  unexpected eof
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>Larger symbols are used in displayed formulas, sum-like symbols have
indices above/below the symbol:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>a</mi><mi>n</mi></msub><mspace width="2.0em"></mspace><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mspace width="0.167em"></mspace><mi>d</mi><mi>x</mi><mspace width="2.0em"></mspace><munderover><mo>∏</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>10</mn></munderover><msub><mi>b</mi><mi>i</mi></msub><mi>…</mi></mrow><annotation encoding="application/x-tex">\sum_{n=1}^N a_n \qquad
\int_0^1f(x)\,dx \qquad
\prod_{i=1}^{10} b_i \ldots</annotation></semantics></math>
</div>
</section>
</section>
<section id="notations">
<h2><a class="toc-backref" href="#toc-entry-20" role="doc-backlink"><span class="sectnum">3 </span>Notations</a></h2>
<section id="top-and-bottom-embellishments">
<h3><a class="toc-backref" href="#toc-entry-21" role="doc-backlink"><span class="sectnum">3.1 </span>Top and bottom embellishments</a></h3>
<p>See <a class="reference internal" href="#accents-and-embellishments">Accents and embellishments</a>.</p>
</section>
<section id="extensible-arrows">
<h3><a class="toc-backref" href="#toc-entry-22" role="doc-backlink"><span class="sectnum">3.2 </span>Extensible arrows</a></h3>
<p>xleftarrow and xrightarrow produce arrows that extend automatically to
accommodate unusually wide subscripts or superscripts. These commands
take one optional argument (the subscript) and one mandatory argument
(the superscript, possibly empty):</p>
<pre class="literal-block">A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</pre>
<p>results in</p>
<pre class="math problematic m">
A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 644)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math 'A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C', rendering as TeX:</p>
<pre class="literal-block">  A \xleftarrow{n+\mu-1} B \xrightarrow[T]
               ^</pre>
<p class="pre-wrap">  unexpected &quot;{&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</section>
<section id="affixing-symbols-to-other-symbols">
<h3><a class="toc-backref" href="#toc-entry-23" role="doc-backlink"><span class="sectnum">3.3 </span>Affixing symbols to other symbols</a></h3>
<p>In addition to the standard <a class="reference internal" href="#accents-and-embellishments">accents and embellishments</a>, other symbols
can be placed above or below a base symbol with the <span class="docutils literal">\overset</span> and
<span class="docutils literal">\underset</span> commands. The symbol is set in &quot;scriptstyle&quot; (smaller font
size). For example, writing <span class="docutils literal"><span class="pre">\overset{*}{X}</span></span> becomes <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>X</mi><mo accent="false">*</mo></mover><annotation encoding="application/x-tex">\overset{*}{X}</annotation></semantics></math>
and <span class="docutils literal"><span class="pre">\underset{+}{M}</span></span> becomes <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><munder><mi>M</mi><mo accent="false">+</mo></munder><annotation encoding="application/x-tex">\underset{+}{M}</annotation></semantics></math>.</p>
</section>
<section id="matrices">
<h3><a class="toc-backref" href="#toc-entry-24" role="doc-backlink"><span class="sectnum">3.4 </span>Matrices</a></h3>
<p>The <span class="docutils literal">matrix</span> and <span class="docutils literal">cases</span> environments can also contain <span class="docutils literal">\\</span> and
<span class="docutils literal">&amp;</span>:</p>
<pre class="literal-block">.. math::
   \left ( \begin{matrix} a &amp; b \\ c &amp; d \end{matrix}\right)</pre>
<p>Result:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">(</mo><mtable><mtr><mtd columnalign="center"><mi>a</mi></mtd><mtd columnalign="center"><mi>b</mi></mtd></mtr><mtr><mtd columnalign="center"><mi>c</mi></mtd><mtd columnalign="center"><mi>d</mi></mtd></mtr></mtable><mo stretchy="true" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\left ( \begin{matrix} a &amp; b \\ c &amp; d \end{matrix} \right)</annotation></semantics></math>
</div>
<p>The environments <span class="docutils literal">pmatrix</span>, <span class="docutils literal">bmatrix</span>, <span class="docutils literal">Bmatrix</span>, <span class="docutils literal">vmatrix</span>, and
<span class="docutils literal">Vmatrix</span> have (respectively) ( ), [ ], { }, | |, and <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="postfix">‖</mo><mspace width="0.222em"></mspace><mo stretchy="false" form="postfix">‖</mo></mrow><annotation encoding="application/x-tex">\Vert\ \Vert</annotation></semantics></math>
delimiters built in, e.g.</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mtable><mtr><mtd columnalign="center"><mi>a</mi></mtd><mtd columnalign="center"><mi>b</mi></mtd></mtr><mtr><mtd columnalign="center"><mi>c</mi></mtd><mtd columnalign="center"><mi>d</mi></mtd></mtr></mtable><mo stretchy="true" form="postfix">)</mo></mrow><mspace width="2.0em"></mspace><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center"><mi>a</mi></mtd><mtd columnalign="center"><mi>b</mi></mtd></mtr><mtr><mtd columnalign="center"><mi>c</mi></mtd><mtd columnalign="center"><mi>d</mi></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow><mspace width="2.0em"></mspace><mrow><mo stretchy="true" form="prefix">∥</mo><mtable><mtr><mtd columnalign="center"><mi>a</mi></mtd><mtd columnalign="center"><mi>b</mi></mtd></mtr><mtr><mtd columnalign="center"><mi>c</mi></mtd><mtd columnalign="center"><mi>d</mi></mtd></mtr></mtable><mo stretchy="true" form="postfix">∥</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{pmatrix} a &amp; b \\ c &amp; d \end{pmatrix} \qquad
\begin{bmatrix} a &amp; b \\ c &amp; d \end{bmatrix} \qquad
\begin{Vmatrix} a &amp; b \\ c &amp; d \end{Vmatrix}</annotation></semantics></math>
</div>
<p>To produce a small matrix suitable for use in text, there is a
<span class="docutils literal">smallmatrix</span> environment
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo minsize="1.2" maxsize="1.2" stretchy="false" form="prefix">(</mo><mtable><mtr><mtd columnalign="center"><mi>a</mi></mtd><mtd columnalign="center"><mi>b</mi></mtd></mtr><mtr><mtd columnalign="center"><mi>c</mi></mtd><mtd columnalign="center"><mi>d</mi></mtd></mtr></mtable><mo minsize="1.2" maxsize="1.2" stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\bigl(\begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix}\bigr)</annotation></semantics></math>
that comes closer to fitting within a single text line than a normal
matrix.</p>
<p>For piecewise function definitions there is a <span class="docutils literal">cases</span> environment:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathvariant="normal"><mi>s</mi><mi>g</mi><mi>n</mi></mstyle><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mrow><mo stretchy="true" form="prefix">{</mo><mtable><mtr><mtd columnalign="left"><mo>−</mo><mn>1</mn></mtd><mtd columnalign="left"><mi>x</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr><mtr><mtd columnalign="left"><mphantom><mo>−</mo></mphantom><mn>1</mn></mtd><mtd columnalign="left"><mi>x</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">\mathrm{sgn}(x) = \begin{cases}
            -1 &amp; x&lt;0\\
  \phantom{-}1 &amp; x&gt;0
\end{cases}</annotation></semantics></math>
</div>
</section>
<section id="spacing-commands">
<h3><a class="toc-backref" href="#toc-entry-25" role="doc-backlink"><span class="sectnum">3.5 </span>Spacing commands</a></h3>
<p>Horizontal spacing of elements can be controlled with the following
commands:</p>
<table>
<tbody>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="2.0em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3\qquad 4</annotation></semantics></math></p></td>
<td></td>
<td><p><span class="docutils literal">3\qquad 4</span></p></td>
<td><p>= 2em</p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="1.0em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3\quad 4</annotation></semantics></math></p></td>
<td></td>
<td><p><span class="docutils literal">3\quad 4</span></p></td>
<td><p>= 1em</p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="0.222em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3~4</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">3~4</span></p></td>
<td><p><span class="docutils literal">3\nobreakspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="0.222em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3\ 4</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">3\ 4</span></p></td>
<td></td>
<td><p>escaped space</p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="0.278em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3\;4</annotation></semantics></math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\;4</span></span></p></td>
<td><p><span class="docutils literal">3\thickspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="0.222em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3\:4</annotation></semantics></math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\:4</span></span></p></td>
<td><p><span class="docutils literal">3\medspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="0.167em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3\,4</annotation></semantics></math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\,4</span></span></p></td>
<td><p><span class="docutils literal">3\thinspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mn>4</mn></mrow><annotation encoding="application/x-tex">3  4</annotation></semantics></math></p></td>
<td><p><span class="docutils literal">3  4</span></p></td>
<td></td>
<td><p>regular space <a class="brackets" href="#footnote-2" id="footnote-reference-6" role="doc-noteref"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></a></p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="-0.167em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3\!4</annotation></semantics></math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\!4</span></span></p></td>
<td><p><span class="docutils literal">3\negthinspace 4</span></p></td>
<td><p>negative space <a class="brackets" href="#footnote-3" id="footnote-reference-7" role="doc-noteref"><span class="fn-bracket">[</span>5<span class="fn-bracket">]</span></a></p></td>
</tr>
<tr><td><p><span class="math problematic m">3\negmedspace 4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\negmedspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><span class="math problematic m">3\negthickspace 4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\negthickspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><span class="math problematic m">3\hspace{1ex}4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\hspace{1ex}4</span></p></td>
<td><p>custom length</p></td>
</tr>
<tr><td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mspace width="1.111em"></mspace><mn>4</mn></mrow><annotation encoding="application/x-tex">3\mspace{20mu}4</annotation></semantics></math></p></td>
<td></td>
<td><p><span class="docutils literal">3\mspace{20mu}4</span></p></td>
<td><p>custom length <a class="brackets" href="#footnote-4" id="footnote-reference-8" role="doc-noteref"><span class="fn-bracket">[</span>6<span class="fn-bracket">]</span></a></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 712)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '3\negmedspace 4', rendering as TeX:</p>
<pre class="literal-block">  3\negmedspace 4
                ^</pre>
<p class="pre-wrap">  unexpected &quot;4&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 713)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '3\negthickspace 4', rendering as TeX:</p>
<pre class="literal-block">  3\negthickspace 4
                  ^</pre>
<p class="pre-wrap">  unexpected &quot;4&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 714)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '3\hspace{1ex}4', rendering as TeX:</p>
<pre class="literal-block">  3\hspace{1ex}4
            ^</pre>
<p class="pre-wrap">  unexpected &quot;x&quot;
  expecting &quot;em&quot;</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-2" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-6">4</a><span class="fn-bracket">]</span></span>
<p>Whitespace characters are ignored in LaTeX math mode.</p>
</aside>
<aside class="footnote brackets" id="footnote-3" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-7">5</a><span class="fn-bracket">]</span></span>
<p>Negative spacing does not work with MathML (last tested in Firefox 115).</p>
</aside>
<aside class="footnote brackets" id="footnote-4" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-8">6</a><span class="fn-bracket">]</span></span>
<p>In LaTeX, the unit must be 'mu' (1 mu = 1/18em).</p>
</aside>
</aside>
<p>There are also three commands that leave a space equal to the height and
width of its argument. For example <span class="docutils literal">\phantom{XXX}</span> results in space as
wide and high as three X’s:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfrac><mrow><mphantom><mrow><mi>X</mi><mi>X</mi><mi>X</mi></mrow></mphantom><mo>+</mo><mn>1</mn></mrow><mrow><mi>X</mi><mi>X</mi><mi>X</mi><mo>−</mo><mn>1</mn></mrow></mfrac><annotation encoding="application/x-tex">\frac{\phantom{XXX}+1}{XXX-1}</annotation></semantics></math>
</div>
<p>The commands <span class="docutils literal">\hphantom</span> and <span class="docutils literal">\vphantom</span> insert space with the
width or height of the argument. They are not supported with <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a>
MathML.</p>
</section>
<section id="modular-arithmetic-and-modulo-operation">
<h3><a class="toc-backref" href="#toc-entry-26" role="doc-backlink"><span class="sectnum">3.6 </span>Modular arithmetic and modulo operation</a></h3>
<p>The commands <span class="docutils literal">\bmod</span>, <span class="docutils literal">\pmod</span>, <span class="docutils literal">\mod</span>, and <span class="docutils literal">\pod</span> deal with the
special spacing conventions of the “mod” notation. <a class="brackets" href="#footnote-5" id="footnote-reference-9" role="doc-noteref"><span class="fn-bracket">[</span>7<span class="fn-bracket">]</span></a></p>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\bmod</span></p></td>
<td><p><span class="docutils literal">\gcd(n,m \bmod n)</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>gcd</mo><mo stretchy="false" form="prefix">(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>mod</mo><mi>n</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\gcd(n,m \bmod n)</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\pmod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \pmod b</span></p></td>
<td><p><span class="math problematic m">x\equiv y \pmod b</span></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \mod c</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>≡</mo><mi>y</mi><mo>mod</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">x\equiv y \mod c</annotation></semantics></math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\pod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \pod d</span></p></td>
<td><p><span class="math problematic m">x\equiv y \pod d</span></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\operatorname{mod}(m,n)</span></span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>mod</mo><mo stretchy="false" form="prefix">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\operatorname{mod}(m,n)</annotation></semantics></math></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 745)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math 'x\equiv y \pmod b', rendering as TeX:</p>
<pre class="literal-block">  x\equiv y \pmod b
                  ^</pre>
<p class="pre-wrap">  unexpected &quot;b&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 747)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math 'x\equiv y \pod d', rendering as TeX:</p>
<pre class="literal-block">  x\equiv y \pod d
                 ^</pre>
<p class="pre-wrap">  unexpected &quot;d&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-5" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-9">7</a><span class="fn-bracket">]</span></span>
<p>Currently <a class="reference external" href="https://sourceforge.net/p/docutils/feature-requests/93/">not supported</a> by the &quot;HTML&quot; <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> option
of the HTML writer.</p>
</aside>
</aside>
</section>
<section id="roots">
<h3><a class="toc-backref" href="#toc-entry-27" role="doc-backlink"><span class="sectnum">3.7 </span>Roots</a></h3>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\sqrt</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\sqrt{x^2-1}</span></span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>1</mn></mrow></msqrt><annotation encoding="application/x-tex">\sqrt{x^2-1}</annotation></semantics></math></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\sqrt[3n]{x^2-1}</span></span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mroot><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>1</mn></mrow><mrow><mn>3</mn><mi>n</mi></mrow></mroot><annotation encoding="application/x-tex">\sqrt[3n]{x^2-1}</annotation></semantics></math></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\sqrt\frac{1}{2}</span></span></p></td>
<td><p><span class="math problematic m">\sqrt\frac{1}{2}</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 767)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\sqrt\frac{1}{2}', rendering as TeX:</p>
<pre class="literal-block">  \sqrt\frac{1}{2}
            ^</pre>
<p class="pre-wrap">  unexpected &quot;{&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</section>
<section id="boxed-formulas">
<h3><a class="toc-backref" href="#toc-entry-28" role="doc-backlink"><span class="sectnum">3.8 </span>Boxed formulas</a></h3>
<p>The command <span class="docutils literal">\boxed</span> puts a box around its argument:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><menclose notation="box"><mrow><mi>η</mi><mo>≤</mo><mi>C</mi><mo stretchy="false" form="prefix">(</mo><mi>δ</mi><mo stretchy="false" form="prefix">(</mo><mi>η</mi><mo stretchy="false" form="postfix">)</mo><mo>+</mo><msub><mi>Λ</mi><mi>M</mi></msub><mo stretchy="false" form="prefix">(</mo><mn>0</mn><mo>,</mo><mi>δ</mi><mo stretchy="false" form="postfix">)</mo><mo stretchy="false" form="postfix">)</mo></mrow></menclose><annotation encoding="application/x-tex">\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}</annotation></semantics></math>
</div>
</section>
</section>
<section id="fractions-and-related-constructions">
<h2><a class="toc-backref" href="#toc-entry-29" role="doc-backlink"><span class="sectnum">4 </span>Fractions and related constructions</a></h2>
<p>The <span class="docutils literal">\frac</span> command takes two ar guments, numerator and denominator,
and typesets them in normal fraction form. For example, <span class="docutils literal">U = <span class="pre">\frac{R}{I}</span></span>
produces <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>U</mi><mo>=</mo><mfrac><mi>R</mi><mi>I</mi></mfrac></mrow><annotation encoding="application/x-tex">U = \frac{R}{I}</annotation></semantics></math>. Use <span class="docutils literal">\dfrac</span> or <span class="docutils literal">\tfrac</span> to
force text style and display style respectively.</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mspace width="1.0em"></mspace><mstyle displaystyle="true"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mstyle><mspace width="1.0em"></mspace><mstyle displaystyle="false"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\frac{x+1}{x-1}  \quad
\dfrac{x+1}{x-1} \quad
\tfrac{x+1}{x-1}</annotation></semantics></math>
</div>
<p>and in text: <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac><annotation encoding="application/x-tex">\frac{x+1}{x-1}</annotation></semantics></math>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle displaystyle="true"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mstyle><annotation encoding="application/x-tex">\dfrac{x+1}{x-1}</annotation></semantics></math>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mstyle displaystyle="false"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mstyle><annotation encoding="application/x-tex">\tfrac{x+1}{x-1}</annotation></semantics></math>.</p>
<p>For binomial expressions such as <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">(</mo><mfrac linethickness="0"><mi>n</mi><mi>k</mi></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\binom{n}{k}</annotation></semantics></math>,
there are <span class="docutils literal">\binom</span>, <span class="docutils literal">\dbinom</span> and <span class="docutils literal">\tbinom</span> commands:</p>
<pre class="literal-block">2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}</pre>
<p>prints</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mi>k</mi></msup><mo>−</mo><mrow><mo stretchy="true" form="prefix">(</mo><mfrac linethickness="0"><mi>k</mi><mn>1</mn></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><msup><mn>2</mn><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mrow><mo stretchy="true" form="prefix">(</mo><mfrac linethickness="0"><mi>k</mi><mn>2</mn></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><msup><mn>2</mn><mrow><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msup></mrow><annotation encoding="application/x-tex">2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}</annotation></semantics></math>
</div>
<p>The <span class="docutils literal">\cfrac</span> command for continued fractions uses displaystyle and
padding for sub-fractions:</p>
<pre class="math problematic m">
\frac{\pi}{4} = 1 + \cfrac{1^2}{
                    2 + \cfrac{3^2}{
                        2 + \cfrac{5^2}{
                            2 + \cfrac{7^2}{2 + \cdots}
                    }}}
\qquad \text{vs.}\qquad
\frac{\pi}{4} = 1 + \frac{1^2}{
                    2 + \frac{3^2}{
                        2 + \frac{5^2}{
                            2 + \frac{7^2}{2 + \cdots}
                    }}}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 805)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\frac{\pi}{4} = 1 + \cfrac{1^2}{</p>
<pre class="literal-block">                      2 + \cfrac{3^2}{
                          2 + \cfrac{5^2}{</pre>
<p class="pre-wrap">                              2 + \cfrac{7^2}{2 + \cdots}
                      }}}
  \qquad \text{vs.}\qquad
  \frac{\pi}{4} = 1 + \frac{1^2}{
                      2 + \frac{3^2}{
                          2 + \frac{5^2}{
                              2 + \frac{7^2}{2 + \cdots}
                      }}}', rendering as TeX:
  pi}{4} = 1 + \cfrac{1^2}{
                     ^
  unexpected &quot;{&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>The optional argument <span class="docutils literal">[l]</span> or <span class="docutils literal">[r]</span> for left or right placement of
the numerator is <a class="reference external" href="https://github.com/w3c/mathml/issues/30">not supported by MathML Core</a>:</p>
<pre class="math problematic m">
\cfrac[l]{x}{x-1} \quad
\cfrac{x}{x-1}    \quad
\cfrac[r]{x}{x-1}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 820)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\cfrac[l]{x}{x-1} \quad</p>
<pre class="literal-block">  \cfrac{x}{x-1}    \quad
  \cfrac[r]{x}{x-1}', rendering as TeX:</pre>
<p class="pre-wrap">  \cfrac[l]{x}{x-1} \quad
        ^
  unexpected &quot;[&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</section>
<section id="delimiter-sizes">
<h2><a class="toc-backref" href="#toc-entry-30" role="doc-backlink"><span class="sectnum">5 </span>Delimiter sizes</a></h2>
<p>Besides the automatic scaling of <a class="reference internal" href="#extensible-delimiters">extensible delimiters</a> with <span class="docutils literal">\left</span>
and <span class="docutils literal">\right</span>, there are four commands to manually select delimiters of
fixed size:</p>
<table>
<tbody>
<tr><td><p>Sizing</p></td>
<td><p>no</p></td>
<td><p><span class="docutils literal">\left</span></p></td>
<td><p><span class="docutils literal">\bigl</span></p></td>
<td><p><span class="docutils literal">\Bigl</span></p></td>
<td><p><span class="docutils literal">\biggl</span></p></td>
<td><p><span class="docutils literal">\Biggl</span></p></td>
</tr>
<tr><td><p>command</p></td>
<td></td>
<td><p><span class="docutils literal">\right</span></p></td>
<td><p><span class="docutils literal">\bigr</span></p></td>
<td><p><span class="docutils literal">\Bigr</span></p></td>
<td><p><span class="docutils literal">\biggr</span></p></td>
<td><p><span class="docutils literal">\Biggr</span></p></td>
</tr>
<tr><td><p>Result</p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">(</mo><mi>b</mi><mo stretchy="false" form="postfix">)</mo><mo stretchy="false" form="prefix">(</mo><mfrac><mi>c</mi><mi>d</mi></mfrac><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\displaystyle
(b)
(\frac{c}{d})</annotation></semantics></math></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>b</mi><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mo stretchy="true" form="prefix">(</mo><mfrac><mi>c</mi><mi>d</mi></mfrac><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">\displaystyle
\left(b\right)
\left(\frac{c}
{d}\right)</annotation></semantics></math></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo minsize="1.2" maxsize="1.2" stretchy="false" form="prefix">(</mo><mi>b</mi><mo minsize="1.2" maxsize="1.2" stretchy="false" form="postfix">)</mo><mo minsize="1.2" maxsize="1.2" stretchy="false" form="prefix">(</mo><mfrac><mi>c</mi><mi>d</mi></mfrac><mo minsize="1.2" maxsize="1.2" stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\displaystyle
\bigl(b\bigr)
\bigl(\frac{c}
{d}\bigr)</annotation></semantics></math></p></td>
<td><p><span class="math problematic m">\displaystyle
\Bigl(b\Bigr)
\Bigl(\frac{c}
{d}\Bigr)</span></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo minsize="2.4" maxsize="2.4" stretchy="false" form="prefix">(</mo><mi>b</mi><mo minsize="2.4" maxsize="2.4" stretchy="false" form="postfix">)</mo><mo minsize="2.4" maxsize="2.4" stretchy="false" form="prefix">(</mo><mfrac><mi>c</mi><mi>d</mi></mfrac><mo minsize="2.4" maxsize="2.4" stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\displaystyle
\biggl(b\biggr)
\biggl(\frac{c}
{d}\biggr)</annotation></semantics></math></p></td>
<td><p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo minsize="3.0" maxsize="3.0" stretchy="false" form="prefix">(</mo><mi>b</mi><mo minsize="3.0" maxsize="3.0" stretchy="false" form="postfix">)</mo><mo minsize="3.0" maxsize="3.0" stretchy="false" form="prefix">(</mo><mfrac><mi>c</mi><mi>d</mi></mfrac><mo minsize="3.0" maxsize="3.0" stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\displaystyle
\Biggl(b\Biggr)
\Biggl(\frac{c}
{d}\Biggr)</annotation></semantics></math></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 840)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\displaystyle</p>
<pre class="literal-block">  \Bigl(b\Bigr)
  \Bigl(\frac{c}</pre>
<p class="pre-wrap">  {d}\Bigr)', rendering as TeX:
  \Bigl(b\Bigr)
       ^
  unexpected &quot;(&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>There are two or three situations where the delimiter size is commonly
adjusted using these commands:</p>
<p>The first kind of adjustment is done for cumulative operators with
limits, such as summation signs. With <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> the
delimiters usually turn out larger than necessary, and using the <span class="docutils literal">Big</span>
or <span class="docutils literal">bigg</span> sizes instead gives better results:</p>
<pre class="math problematic m">
\left[\sum_i a_i\left\lvert\sum_j x_{ij}\right\rvert^p\right]^{1/p}
\text{ versus }
\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 854)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\left[\sum_i a_i\left\lvert\sum_j x_{ij}\right\rvert^p\right]^{1/p}</p>
<pre class="literal-block">  \text{ versus }
  \biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}', rendering as TeX:</pre>
<p class="pre-wrap">  ggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\B
                     ^
  unexpected &quot;\\&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>The second kind of situation is clustered pairs of delimiters, where
left and right make them all the same size (because that is adequate to
cover the encompassed material), but what you really want is to make some
of the delimiters slightly larger to make the nesting easier to see.</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo><mo>−</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>b</mi><mn>2</mn></msub><mo stretchy="false" form="postfix">)</mo><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mo stretchy="true" form="prefix">(</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo><mo>+</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mn>2</mn></msub><mo stretchy="false" form="postfix">)</mo><mo stretchy="true" form="postfix">)</mo></mrow><mspace width="1.0em"></mspace><mtext mathvariant="normal">versus</mtext><mspace width="1.0em"></mspace><mo minsize="1.2" maxsize="1.2" stretchy="false" form="prefix">(</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo><mo>−</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>b</mi><mn>2</mn></msub><mo stretchy="false" form="postfix">)</mo><mo minsize="1.2" maxsize="1.2" stretchy="false" form="postfix">)</mo><mo minsize="1.2" maxsize="1.2" stretchy="false" form="prefix">(</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo><mo>+</mo><mo stretchy="false" form="prefix">(</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mn>2</mn></msub><mo stretchy="false" form="postfix">)</mo><mo minsize="1.2" maxsize="1.2" stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\left((a_1 b_1) - (a_2 b_2)\right)
\left((a_2 b_1) + (a_1 b_2)\right)
\quad\text{versus}\quad
\bigl((a_1 b_1) - (a_2 b_2)\bigr)
\bigl((a_2 b_1) + (a_1 b_2)\bigr)</annotation></semantics></math>
</div>
<p>The third kind of situation is a slightly oversize object in running
text, such as <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">|</mo><mfrac><mrow><mi>b</mi><mi>′</mi></mrow><mrow><mi>d</mi><mi>′</mi></mrow></mfrac><mo stretchy="true" form="postfix">|</mo></mrow><annotation encoding="application/x-tex">\left|\frac{b&#39;}{d&#39;}\right|</annotation></semantics></math> where the delimiters produced
by <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> cause too much line spreading. <a class="brackets" href="#footnote-6" id="footnote-reference-10" role="doc-noteref"><span class="fn-bracket">[</span>8<span class="fn-bracket">]</span></a> In that case
<span class="docutils literal">\bigl</span> and <span class="docutils literal">\bigr</span> can be used to produce delimiters that are larger
than the base size but still able to fit within the normal line spacing:
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo minsize="1.2" maxsize="1.2" stretchy="false" form="prefix">|</mo><mfrac><mrow><mi>b</mi><mi>′</mi></mrow><mrow><mi>d</mi><mi>′</mi></mrow></mfrac><mo minsize="1.2" maxsize="1.2" stretchy="false" form="prefix">|</mo></mrow><annotation encoding="application/x-tex">\bigl|\frac{b&#39;}{d&#39;}\bigr|</annotation></semantics></math>.</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-6" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-10">8</a><span class="fn-bracket">]</span></span>
<p>With MathML, an example would be parentheses
around a <span class="docutils literal">smallmatrix</span> environment
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">(</mo><mtable><mtr><mtd columnalign="center"><mi>a</mi></mtd><mtd columnalign="center"><mi>b</mi></mtd></mtr><mtr><mtd columnalign="center"><mi>c</mi></mtd><mtd columnalign="center"><mi>d</mi></mtd></mtr></mtable><mo stretchy="true" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\left(\begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix}\right)</annotation></semantics></math>
vs. <span class="math problematic m">\Bigl(\begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix}\Bigr)</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 877)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\Bigl(\begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix}\Bigr)', rendering as TeX:</p>
<pre class="literal-block">  \Bigl(\begin{smallmatrix} a &amp; b \\ c &amp; d
       ^</pre>
<p class="pre-wrap">  unexpected &quot;(&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
</aside>
</aside>
</section>
<section id="text">
<h2><a class="toc-backref" href="#toc-entry-31" role="doc-backlink"><span class="sectnum">6 </span>Text</a></h2>
<p>The main use of the command <span class="docutils literal">\text</span> is for words or phrases in a
display. It is similar to <span class="docutils literal">\mbox</span> in its effects but, unlike <span class="docutils literal">\mbox</span>,
automatically produces subscript-size text if used in a subscript,
<span class="docutils literal"><span class="pre">k_{\text{B}}T</span></span> becomes <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mtext mathvariant="normal">B</mtext></msub><mi>T</mi></mrow><annotation encoding="application/x-tex">k_{\text{B}}T</annotation></semantics></math>.</p>
<p>Whitespace is kept inside the argument:</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mo stretchy="false" form="prefix">[</mo><msub><mi>x</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false" form="postfix">]</mo></mrow></msub><mrow><mspace width="0.333em"></mspace><mtext mathvariant="normal"> is monotonic for </mtext><mspace width="0.333em"></mspace></mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mspace width="0.167em"></mspace><mi>…</mi><mo>,</mo><mspace width="0.167em"></mspace><mi>c</mi><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">f_{[x_{i-1},x_i]} \text{ is monotonic for }  i = 1,\,\ldots ,\,c+1</annotation></semantics></math>
</div>
<p>The text may contain math commands wrapped in <span class="docutils literal">$</span> signs, e.g.</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">(</mo><mo>−</mo><mn>1</mn><msup><mo stretchy="false" form="postfix">)</mo><msub><mi>n</mi><mi>i</mi></msub></msup><mo>=</mo><mrow><mo stretchy="true" form="prefix">{</mo><mtable><mtr><mtd columnalign="left"><mo>−</mo><mn>1</mn><mspace width="1.0em"></mspace><mrow><mrow><mtext mathvariant="normal">if </mtext><mspace width="0.333em"></mspace></mrow><msub><mi>n</mi><mi>i</mi></msub><mrow><mspace width="0.333em"></mspace><mtext mathvariant="normal"> is odd,</mtext></mrow></mrow></mtd></mtr><mtr><mtd columnalign="left"><mo>+</mo><mn>1</mn><mspace width="1.0em"></mspace><mrow><mrow><mtext mathvariant="normal">if </mtext><mspace width="0.333em"></mspace></mrow><msub><mi>n</mi><mi>i</mi></msub><mrow><mspace width="0.333em"></mspace><mtext mathvariant="normal"> is even.</mtext></mrow></mrow></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">(-1)^{n_i} = \begin{cases} -1 \quad \text{if $n_i$ is odd,} \\
              +1 \quad \text{if $n_i$ is even.}
\end{cases}</annotation></semantics></math>
</div>
<!-- TODO ignore {}, handle text-mode commands -->
</section>
<section id="integrals-and-sums">
<h2><a class="toc-backref" href="#toc-entry-32" role="doc-backlink"><span class="sectnum">7 </span>Integrals and sums</a></h2>
<p>The limits on integrals, sums, and similar symbols are placed either to
the side of or above and below the base symbol, depending on convention
and context. In inline formulas and fractions, the limits on sums, and
similar symbols like</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></munder><munderover><mo>∑</mo><mn>1</mn><mi>n</mi></munderover><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow><annotation encoding="application/x-tex">\lim_{n\to\infty} \sum_1^n \frac{1}{n}</annotation></semantics></math>
</div>
<p>move to index positions: <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><msubsup><mo>∑</mo><mn>1</mn><mi>n</mi></msubsup><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow><annotation encoding="application/x-tex">\lim_{n\to\infty} \sum_1^n \frac{1}{n}</annotation></semantics></math>.</p>
<section id="altering-the-placement-of-limits">
<h3><a class="toc-backref" href="#toc-entry-33" role="doc-backlink"><span class="sectnum">7.1 </span>Altering the placement of limits</a></h3>
<p>The commands <span class="docutils literal">\intop</span> and <span class="docutils literal">\ointop</span> produce integral signs with
limits as in sums and similar: <span class="math problematic m">\intop_0^1</span>, <span class="math problematic m">\ointop_c</span> and</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 921)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\intop_0^1', rendering as TeX:</p>
<pre class="literal-block">  \intop_0^1
        ^</pre>
<p class="pre-wrap">  unexpected &quot;_&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 921)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\ointop_c', rendering as TeX:</p>
<pre class="literal-block">  \ointop_c
         ^</pre>
<p class="pre-wrap">  unexpected &quot;_&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<pre class="math problematic m">
\intop_0^1 \quad \ointop_c
   \quad \text{vs.} \quad
\int^1_0   \quad \oint_c
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 924)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\intop_0^1 \quad \ointop_c</p>
<pre class="literal-block">     \quad \text{vs.} \quad
  \int^1_0   \quad \oint_c', rendering as TeX:</pre>
<p class="pre-wrap">  \intop_0^1 \quad \ointop_c
        ^
  unexpected &quot;_&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<p>The commands <span class="docutils literal">\limits</span> and <span class="docutils literal">\nolimits</span> override the default placement
of the limits for any operator; <span class="docutils literal">\displaylimits</span> forces standard
positioning as for the sum command. They should follow immediately after
the operator to which they apply.</p>
<p>Compare the same term with default positions, <span class="docutils literal">\limits</span>, and
<span class="docutils literal">\nolimits</span> in inline and display mode: <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></msub><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\lim_{x\to0}f(x)</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></munder><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\lim\limits_{x\to0}f(x)</annotation></semantics></math>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></msub><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\lim\nolimits_{x\to0}f(x)</annotation></semantics></math>, vs.</p>
<div>
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></munder><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mo>,</mo><mspace width="1.0em"></mspace><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></munder><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mspace width="1.0em"></mspace><msub><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></msub><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mi>.</mi></mrow><annotation encoding="application/x-tex">\lim_{x\to0}f(x), \quad
\lim\limits_{x\to0}f(x) \quad
\lim\nolimits_{x\to0}f(x).</annotation></semantics></math>
</div>
<!-- TODO: \substack -->
<!-- TODO: \sideset -->
</section>
</section>
<section id="changing-the-size-of-elements-in-a-formula">
<h2><a class="toc-backref" href="#toc-entry-34" role="doc-backlink"><span class="sectnum">8 </span>Changing the size of elements in a formula</a></h2>
<p>The declarations <a class="brackets" href="#footnote-7" id="footnote-reference-11" role="doc-noteref"><span class="fn-bracket">[</span>9<span class="fn-bracket">]</span></a> <span class="docutils literal">\displaystyle</span>, <span class="docutils literal">\textstyle</span>,
<span class="docutils literal">\scriptstyle</span>, and <span class="docutils literal">\scriptscriptstyle</span>, select a symbol size and
spacing that would be applied in display math, inline
math, first-order subscript, or second-order subscript, respectively
even when the current context would normally yield some other size.</p>
<p>For example <span class="docutils literal"><span class="pre">:math:`\displaystyle</span> <span class="pre">\sum_{n=0}^\infty</span> <span class="pre">\frac{1}{n}`</span></span> is printed as <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mi>∞</mi></msubsup><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow><annotation encoding="application/x-tex">\displaystyle \sum_{n=0}^\infty \frac{1}{n}</annotation></semantics></math>
rather than <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mi>∞</mi></msubsup><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow><annotation encoding="application/x-tex">\sum_{n=0}^\infty \frac{1}{n}</annotation></semantics></math> and</p>
<pre class="literal-block">\frac{\scriptstyle\sum_{n &gt; 0} z^n}
{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}</pre>
<p>yields</p>
<pre class="math problematic m">
\frac{\scriptstyle\sum_{n &gt; 0} z^n}
{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}
\text{ instead of the default }
\frac{\sum_{n &gt; 0} z^n}
{\prod_{1\leq k\leq n} (1-q^k)}.
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 964)</p>
<p>TeX to MathML converter `pandoc` failed:</p>
<p>[WARNING] Could not convert TeX math '\frac{\scriptstyle\sum_{n &gt; 0} z^n}</p>
<pre class="literal-block">  {\displaystyle\prod_{1\leq k\leq n} (1-q^k)}
  \text{ instead of the default }</pre>
<p class="pre-wrap">  \frac{\sum_{n &gt; 0} z^n}
  {\prod_{1\leq k\leq n} (1-q^k)}.', rendering as TeX:
  \frac{\scriptstyle\sum_{n &gt; 0} z^n}
                    ^
  unexpected &quot;\\&quot;
  expecting &quot;%&quot;, &quot;\\label&quot;, &quot;\\nonumber&quot; or whitespace</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-7" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-11">9</a><span class="fn-bracket">]</span></span>
<p>&quot;Declarations&quot; are commands that affect processing of the current
&quot;group&quot;. In particular, notice where the braces fall that delimit the
effect of the command: Right: <span class="docutils literal">{\displaystyle <span class="pre">...}</span></span> Wrong:
<span class="docutils literal"><span class="pre">\displaystyle{...}</span></span>.</p>
<p>With <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> MathML, the declaration must be the first element
after the opening bracket.</p>
</aside>
</aside>
<div role="list" class="citation-list">
<div class="citation" id="iso-80000-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#citation-reference-1">ISO-80000-2</a><span class="fn-bracket">]</span></span>
<p><cite>Quantities and units – Part 2: Mathematical signs
and symbols to be used in the natural sciences and technology</cite>:
<a class="reference external" href="http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887">http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887</a>.</p>
</div>
</div>
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